{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm\n",
    "import numpy as np\n",
    "from math import sin, cos, pi\n",
    "\n",
    "def plot_function(f,xmin,xmax,**kwargs):\n",
    "    ts = np.linspace(xmin,xmax,1000)\n",
    "    plt.plot(ts,[f(t) for t in ts],**kwargs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1 Testing a projectile simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 Building a simulation with Euler’s method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def trajectory(theta,speed=20,height=0,dt=0.01,g=-9.81):\n",
    "    vx = 20 * cos(pi * theta / 180)\n",
    "    vz = 20 * sin(pi * theta / 180)\n",
    "    t,x,z = 0, 0, height\n",
    "    ts, xs, zs = [t], [x], [z]\n",
    "    while z >= 0:\n",
    "        t += dt\n",
    "        vz += g * dt\n",
    "        x += vx * dt\n",
    "        z += vz * dt\n",
    "        ts.append(t)\n",
    "        xs.append(x)\n",
    "        zs.append(z)\n",
    "    return ts, xs, zs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_trajectories(*trajs,show_seconds=False):\n",
    "    for traj in trajs:\n",
    "        xs, zs = traj[1], traj[2]\n",
    "        plt.plot(xs,zs)\n",
    "        if show_seconds:\n",
    "            second_indices = []\n",
    "            second = 0\n",
    "            for i,t in enumerate(traj[0]):\n",
    "                if t>= second:\n",
    "                    second_indices.append(i)\n",
    "                    second += 1\n",
    "            plt.scatter([xs[i] for i in second_indices], [zs[i] for i in second_indices])\n",
    "    xl = plt.xlim()\n",
    "    plt.plot(plt.xlim(),[0,0],c='k')\n",
    "    plt.xlim(*xl)\n",
    "    \n",
    "    width = 7\n",
    "    coords_height = (plt.ylim()[1] - plt.ylim()[0])\n",
    "    coords_width = (plt.xlim()[1] - plt.xlim()[0])\n",
    "    plt.gcf().set_size_inches(width , width * coords_height / coords_width)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x190.027 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_trajectories( \n",
    "    trajectory(45),\n",
    "    trajectory(60))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 Measuring properties of the trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def landing_position(traj):\n",
    "    return traj[1][-1]\n",
    "\n",
    "def hang_time(traj):\n",
    "    return traj[0][-1] #<1>\n",
    "\n",
    "def max_height(traj):\n",
    "    return max(traj[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.3 Exploring different launch angles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x22a9ed3f4a8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "angles = range(0,90,5)\n",
    "landing_positions = [landing_position(trajectory(theta)) for theta in angles]\n",
    "plt.scatter(angles,landing_positions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.4 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** How far does the cannonball go when fired at an angle of 50 degrees from an initial height of zero?  How about if it is fired at an angle of 130 degrees?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40.10994684444007"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "landing_position(trajectory(50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-40.10994684444007"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "landing_position(trajectory(130))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mini-project:** Enhance the `plot_trajectories` function in the source code to draw a large dot on the trajectory graph at each passing second, so we can see the passing of time on the plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See implementation above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x249.538 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_trajectories(\n",
    "    trajectory(20), \n",
    "    trajectory(45),\n",
    "    trajectory(60),\n",
    "    trajectory(80), \n",
    "    show_seconds=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Make a scatterplot of hang time versus angle, for angles between 0 and 180 degrees.  What launch angle produces the maximum hang time?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x22a9edba5f8>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_angles = range(0,181,5)\n",
    "hang_times = [hang_time(trajectory(theta)) for theta in test_angles]\n",
    "plt.scatter(test_angles, hang_times)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mini-project:** Write a function `plot_trajectory_metric` which plots the result of any metric we want over a given set of theta values.  For instance `plot_trajectory_metric(landing_position,[10,20,30])` should make a scatter plot of landing positions versus launch angle for launch angles of 10, 20, and 30 degrees.  \n",
    "\n",
    "As a bonus, pass the keyword arguments from `plot_trajectory_metric` to the internal calls of the trajectory function, so you could re-run the test with a different simulation parameter. For instance, `plot_trajectory_metric(landing_position,[10,20,30], height=10)` would make the same plot, but simulated with a 10 meter initial launch height."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_trajectory_metric(metric,thetas,**settings):\n",
    "    plt.scatter(thetas,[metric(trajectory(theta,**settings)) for theta in thetas])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_trajectory_metric(hang_time, range(0,181,5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mini-project:** What is the approximate launch angle that yields the greatest range for the cannonball with a 10 meter initial launch height?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_trajectory_metric(landing_position,range(0,90,5), height=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2 Calculating the optimal range"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 Finding the projectile range as a function of the launch angle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x22a9eedc160>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "trj = trajectory(45)\n",
    "ts, zs = trj[0], trj[2]\n",
    "plt.plot(ts,zs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def z(t): #<1>\n",
    "    return 20*sin(45*pi/180)*t + (-9.81/2)*t**2\n",
    "\n",
    "plt.plot(ts,zs)\n",
    "plot_function(z,0,2.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def r(theta):\n",
    "    return (-2*20*20/-9.81)*sin(theta*pi/180)*cos(theta*pi/180)\n",
    "\n",
    "plot_function(r,0,90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Solving for the maximum range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40.774719673802245"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r(45)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-40.77471967380224"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r(135)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 Identifying maxima and minima"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3 Enhancing our simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.1 Adding another dimension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def trajectory3d(theta,phi,speed=20,height=0,dt=0.01,g=-9.81):\n",
    "    vx = 20 * cos(pi * theta / 180) * cos(pi * phi / 180)\n",
    "    vy = 20 * cos(pi * theta / 180) * sin(pi * phi / 180)\n",
    "    vz = 20 * sin(pi * theta / 180)\n",
    "    t,x,y,z = 0, 0, 0, height\n",
    "    ts, xs, ys, zs = [t], [x], [y], [z]\n",
    "    while z >= 0:\n",
    "        t += dt\n",
    "        vz += g * dt\n",
    "        x += vx * dt\n",
    "        y += vy * dt\n",
    "        z += vz * dt\n",
    "        ts.append(t)\n",
    "        xs.append(x)\n",
    "        ys.append(y)\n",
    "        zs.append(z)\n",
    "    return ts, xs, ys, zs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_trajectory3d(traj):\n",
    "    fig, ax = plt.gcf(), plt.gca()\n",
    "    fig.set_size_inches(7,7)\n",
    "    ax = fig.gca(projection='3d')\n",
    "    ax.plot(traj[1],traj[2],traj[3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Paul\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:4: UserWarning: Requested projection is different from current axis projection, creating new axis with requested projection.\n",
      "  after removing the cwd from sys.path.\n",
      "C:\\Users\\Paul\\Anaconda3\\lib\\site-packages\\matplotlib\\cbook\\deprecation.py:107: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance.  In a future version, a new instance will always be created and returned.  Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n",
      "  warnings.warn(message, mplDeprecation, stacklevel=1)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_trajectory3d(trajectory3d(45,45))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2 Modeling terrain around the cannon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def flat_ground(x,y):\n",
    "    return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ridge(x,y):\n",
    "    return (x**2 - 5*y**2) / 2500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def trajectory3d(theta,phi,speed=20,height=0,dt=0.01,g=-9.81,elevation=flat_ground):\n",
    "    vx = speed * cos(pi * theta / 180) * cos(pi * phi / 180)\n",
    "    vy = speed * cos(pi * theta / 180) * sin(pi * phi / 180)\n",
    "    vz = speed * sin(pi * theta / 180)\n",
    "    t,x,y,z = 0, 0, 0, height\n",
    "    ts, xs, ys, zs = [t], [x], [y], [z]\n",
    "    while z >= elevation(x,y):\n",
    "        t += dt\n",
    "        vz += g * dt\n",
    "        x += vx * dt\n",
    "        y += vy * dt\n",
    "        z += vz * dt\n",
    "        ts.append(t)\n",
    "        xs.append(x)\n",
    "        ys.append(y)\n",
    "        zs.append(z)\n",
    "    return ts, xs, ys, zs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_trajectories_3d(*trajs,elevation=flat_ground,bounds=None,zbounds=None,shadows=False):\n",
    "    fig, ax = plt.gcf(), plt.gca(projection='3d')\n",
    "    fig.set_size_inches(7,7)    \n",
    "\n",
    "    if not bounds:\n",
    "        xmin = min([x for traj in trajs for x in traj[1]])\n",
    "        xmax = max([x for traj in trajs for x in traj[1]])\n",
    "        ymin = min([x for traj in trajs for x in traj[2]])\n",
    "        ymax = max([x for traj in trajs for x in traj[2]])\n",
    "\n",
    "        padding_x = 0.1 * (xmax-xmin)\n",
    "        padding_y = 0.1 * (ymax-ymin)\n",
    "        xmin -= padding_x\n",
    "        xmax += padding_x\n",
    "        ymin -= padding_y\n",
    "        ymax += padding_x\n",
    "    \n",
    "    else:\n",
    "        xmin, xmax, ymin, ymax = bounds\n",
    "    \n",
    "\n",
    "    plt.plot([xmin,xmax],[0,0],[0,0],c='k')\n",
    "    plt.plot([0,0],[ymin,ymax],[0,0],c='k')\n",
    "\n",
    "    g = np.vectorize(elevation)\n",
    "    ground_x = np.linspace(xmin, xmax, 20)\n",
    "    ground_y = np.linspace(ymin, ymax, 20)\n",
    "    ground_x, ground_y = np.meshgrid(ground_x,ground_y)\n",
    "    ground_z = g(ground_x,ground_y)\n",
    "    ax.plot_surface(ground_x, ground_y, ground_z, cmap=cm.coolwarm, alpha=0.5,\n",
    "                       linewidth=0, antialiased=True)\n",
    "    for traj in trajs:\n",
    "        ax.plot(traj[1],traj[2],traj[3])\n",
    "        if shadows:\n",
    "            ax.plot([traj[1][0],traj[1][-1]],[traj[2][0],traj[2][-1]],[0,0],c='gray',linestyle='dashed')\n",
    "    \n",
    "    if zbounds:\n",
    "        ax.set_zlim(*zbounds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0a70g6fj4OCMjI4yNjeF2u5FleV5a3AsRw8JZZMSbGKA/aNH6uly8eJHmlmZ+MvYT3Jqb/9j9H+TaEqsccM2Ka/jopo/yUMND1BbVcsuaW6bcM90DHo9LZsYbhc+F7ckPoYlmLl7/XdSJ5G6UqXJXqUWbcN/0Tey/+RDWF/4Rz3Vfien+UAvI5XLR2NjI+Pg4Fy5cCFhAegzIYrEkvMZkorfOSJRIBUkbGhpYtmwZGRkZhgWUBAzBWSRomobL5QIml5KPRjRrQlVVTp06xejoKGdzz9JwoYEPFHyAtTmxn/cQBGHK2Z27K+/m9f7XeeDYA2wt2MrKrJWTrk8GyRjHevAfEC+ewvXun6JkFsNEbxJW5ifV35rldTfhrf4wltcfQVleg1wxVdijIYoiFouF1atXA34X3OjoKMPDwwkL0EzFYTbG1AVIUZRAlptREXvmGO/QIkC3ak6cOBE4GBcr0x3knJiY4MiRI5jNZpZtWMbDzQ9zddHV7MjYEdf6womaKIjcX3c/VsnKFw9/EVVTp70+UWYyjqnlCSyNP8db9zGUlXsWxDfaUOvBs/tzyMtrsT3/GYSh0zMeT5IkcnNzJ7ngCgoKGB8fp7GxkaNHj9La2jqtCy5ViQip2PB1IdOtn2Bx0QVoYmKC0dFRRkdHcblcgZqEBlMxBGcBo6d+ejyewIMR7wYbTnD0bpwnTpygoqKC1atX860T3wLgc9s/F/c6IwlIYVohf7Ptb2i82MhvOn4T9frZRBjuwPb83yIX1+Dd+TdzupYZIZlx3/xdNMmK/emPg+KLfk8Q0cQhnAAVFhYyMTERUYAWSqq1Pm44d3M4AdIrYgcLkNPpNAQoCMOltkDREwMURZnkf473gx26uft8PpqbmxFFMdCN83j/cQ5eOMhHqj7CsoxlnFPPzWiOYG5ceSO/Pv1rvn3i2+wv2U+ONWfus9RUBfsznwhs1sEla+ZaCKMRbjPXMpfhecu/Yv/Nh7C89g1/ZYQZjDcdugDl5uZSVlYWcME5HA66urqQZTngdvN6vQnFgMKRCjcd+F2IsYwbLgtOP5JgFCS9jGHhLEBUVcXj8UwSG0isOVrwPcPDwxw5coTCwkI2bdqEyWRC1VQePP4gRfYi3r/h/Qlt4tEqB3x2+2cZ943zSMMjUa+fDczHvo/Ucxz3NV9GyypO2TyzecZFXncTvo23Yjn8bcTuN2Y8XqzoAlRWVsbWrVvZvn07OTk5KIpCU1NTwALq6+sL9MpJhFQJTqLjhrOAwC+yDoeDxsZGxsbGcDqdgXNy8/3LTDIwLJwFRLSKATMRnNOnTzM4OMjWrVtJS0sL/P7ghYO0DLfwpbovhT0zEwvRBGRtzlreseYdPHH6Ce7YcMecWjjCUAfWP34N35q3IG94+4zXMJ9wH/hH0s+/iu25v8H5gefAZI16T7JFURRF0tLSUFWVsrIyVFUNJCF0d3fj8/nIysoKnAOyWqOvMRXrTPa4wWd9dLcbXC5ICuG7oi42C8gQnAVCLA3SEhEcRVFoaGigoKCAmpqaSSKmaRo/bPohKzNX8taVb0147bHElu7ZeA9PnnmS7zd+nzsL75ybWmqaiu13nwLJhue6f563hzunY9oN0pqJ+7qvkvbEB7AcfQjv1X89s/ESJDjeIopiIMNN/53uggsWoJycHHJzcyMKUKosHEj+Z05RlIBLLbQe3GKviG0IzjwnnooB8QpOb28vQ0NDlJeXs2LFiim/f6n7Jdocbdxfdz+SOP05nemIxdIosBdw69pb+WnbT7k261rW2NZMuUaPL7ndbvLy8sjNzSUjIyPiRhOvhWN+80eYuo7guuFBtIylMd+XKHPhQlHKDuDb8HYsh7+NXP421CXTp7fPdkZZsACtWrUKVVUZGxtjeHiY5ubmiAKUSsFJNpHWGk6A9APc3/rWt9iwYQPvec97ZnOpSccQnHlMvHXQYs1Sk2WZkydP4vP5KCoqIiNjarUATdP4QdMPWJ6+fEbWDYQ/hxOOuyvv5onTT/BE9xN8OmdyYHtkZITGxkZWrVpFeno6IyMjXLhwgbGxMex2eyBQnZ6enlgV7IkBrC9/DXnlXuSNt8Z9f6LMRZ0yz/77MXW+gPX5z+J6739HrZwwl7XURFEkOzub7OzsKQLU0tIyqSXBQskE0y2caAQL0MTERMzuxfmMITjzFN2qiaeVQCwWzujoKI2NjZSWlrJ8+XJaW1vD3nNi8ARNQ018rvpzUdsJRCNWSyPHmsMta27h560/507XnRRTjKZpnD17lt7eXrZu3YrVasXn85GWlsayZcsCB14dDgdnz55lfHyctLS0QAwg1k3I+tK/gOzGfc30ddIWQ2BXSy/As/fvsf3u05gbfo5v8+2Rr51nVQGCBUgfa2xsjK6uLhwOB0eOHCEzMzPw97fZEos7ppJEXr/T6ZwUW12oGIIzz9ATA3RRCGd9RGI6wdE37p6eHjZv3hwYN5L18YtTvyDTnMnNq25O7IUEEY9r6/by2/l56895sutJNq7YSGNjI3a7ndraWkRRRFGUKWOnpaWRlpZGcbFfoJxOJ8PDw3R0dDAxMUFTU1PAArLb7VPmFHuOYW76BZ6ae9HyprrygudaCMSyTl/VbZiafonl5X/BV34z2LLDXpeK8y3JPKSpC5DH4yEtLY3S0lLGxsZwOBycPHkSr9c77wQollJSoUxMTJCenp6iFc0ehuDMI4ITAxRFSehMTbh7PB4PjY2NpKenU1dXN+lhD+eGG3ANcPD8QW4rvw27aeoGHS/xCM7S9KXszt/N73p/x9WHr2Zz+WaKiorimis9PZ309HSWL1/O0aNHKS0tZXh4mLa2NjweT2ADys3NxWo2YfvD36OmF+Hd8YlEX+LCQxDwHPgSaT++Eetr38Kz/x/CXrZQ2hPoVkOwBbRy5cqABeRwOGhtbQ38/fUY0HQClCprNtazPcG4XC7DwjFIDqGJAfqDM5MzNToDAwO0tbVRXl5OQUFBTPc80f4EqqZy69rkxDLiERxN09iXto9Dg4c4n3Oe64uun/HcmZmZZGZmUlpaOiUIXXD+aSr66unb/RVMWEjOMcTYmGv3nFpUha/qvZiP/xDvVXeg5a6ecs1CqQoQyU0VToDGx8cZHh6OKkCpPEwar4XjdDrj8nbMVwzBmWMiJQYkKji6aKmqSmtrK06nk+rq6ogBx1AxkFWZJ04/wa7iXZRkliT4qqafIxIej4eGhgaWW5azIXMDT559krur7kZMsB1ApNTxQBB6eSHph+/BU7iF3vzdOBobURQlkCWVSEvmZKxxNvHu/gzm1iexvvgV3Lf8IOw189mlFjxmrHHOrKwssrKyIgpQRkZG1AzImaCqKiZTfFuvEcMxmDH6Ic5wiQEzsXDGx8cDZdU3bNgw7YMYOs9rva9x0X2RW1bHX1l4ujmiCc7Fixc5efIk5eXleL1ebuAGvtn+TY70HWHH0viKhcaK5dgPECf6Ud72CKuX+2M34Voy699+4/1WuhDQ0gvx1v0l1pf/Bd/Zl1FW7p78+wVk4cS7iUNkAXI4HLS3tzM6Okpzc3MgBhQuBhgvhoVjMKtEqxgAiQmOIAgMDw/T29tLVVUVWVlZUe8JFYPfdPyGXGsuu4t3T3NXfBvRdBaOpmmcPn2aoaEhtm/fjs1mo7u7m7rcOnKsOfyq/VcpERzBOYTlyEP41tyAsrwm8PPQfjCyLONwOBgaGmJoaAifz0dHRwe5ublkZWUtChHybv9zzPU/wfriP+H8wDOT0qRT4fZLhYWTLPdXsAAVFBRw6tQpSkpKcDgcgRhgRkbGJBdcvOKZyFpdLldSxG6uMQRnlomlYgDELzher5fOzk5UVaWuri7mjTA40cDhcXCo+xDvWfeeaVOhdQGJR3DCvRa3201DQwM5OTlUV1cHHkJBEDAJJv607E/5SetP6Hf2U5hWOOX+mWA58m3wTeDd89lprzOZTOTn5we6YJ47d46MjAz6+/tpb2/HZDIFEhAyMzPj2kjmOoYTwGTDs+tvsD/zV5jankZe/yeBXy2UpIFUWWKSJAUEqLS0FE3TAi64U6dO4Xa74xagRCwcTdMSsuDmGwv/FSwQYrFqgpEkaUoKcCSGhoZoaWmhsLAw7pTL4LjPs2efRVZl3lb2tqj3xPMtLZyFMzg4SGtrKxs2bGDJkiVhr3/nmnfy6MlHebrzae6uvDvwu5kijF7A/OaP8G18D+qS8vjuFQQKCwspLPQLoMfjCdQBGxsbw2q1BgQoIyMj6nrnOoajI294B8qRh7C88gDyuhvhUmWJuYy3xMNsNXULTUKZToB0F1zoa11IVRGSjSE4s0C8FQMgNgtHL7o5PDzM9u3bcblc9PbG15EyWAye7nya8pxy1uWsi/meeOdQVZX29nZGRkamTWYAKMks4ar8q3i682nuqrgraZuU9ZX/B4KAd+cn47ov3PxWq5WlS5eydKm/FI5+CPX8+fNJq4IwK4gS3p1/g/3JD2Nq+TXyxncDC1scZmPMSAKkx4Dcbjfp6emTYkDxWjjzxhJOAobgpBA93bmjo4MVK1bE1f8i3CHHYJxOJw0NDeTn51NTU4MgCIFGbPGgC1vXeBfNQ8385VV/GfM9saK71FwuF/X19eTn51NdXR3xvQgWqJtW3cRXX/8qrcOtbMjbEPOcEdcycg5T8y/xbb0bLTP5rQfsdjt2u31SFYTh4WE6OzsDh/d0AZpvG4m87iaUwiqsrz6IvOFPQbKkLIazUFxq8YpYsACtWLEirAD5fD4GBgYQBCGsBRSOVFXDnm0MwUkRwS60rq4uVq5cGdf9wa6uULq7uzlz5gwbN24MVNmF2GuWhc6jqirPn38egOtXRD/3koiFMzo6yoULF6ioqAgE5GMZ//rS63ng2AP8tvO3SREcy+HvgGjCW3PvjMeKRnAVhOXLl6NpGhMTEwwPD9Pe3s7ExASaptHT0xP1EOKsIAh4dn2atF/fhbnxF/iu+sCCylKbj1ZTOAE6duwYAKdPn8blcpGenh6IAUVywS0GsQFDcFKCqqp4vd5J6c7xfnjDWRGyLNPc3IymadTV1U0JIs6k4+fz555nY95GijOif+uPp5W1qqr09PTgcrmoq6uLqcNjsOBkWbLYU7yH584+xye2fAJxBj0DhdELmJv+G9/m22elGvSU+QWBjIwMMjIyWLFiBWNjY3R0dOD1egNlWPReMLm5uUnrhhkPStk1KMXVWF77Fr6q9856tehESZXgJDsLUd8PSkpKMJlMk76EnD59OpD+HCxAi6XKABiCk1QiJQbEG2QPvkfH4XDQ3NzMqlWrKC4OLwqJnt3pdnXTOtzKX235q5juidWScjqd1NfXB+IYsW6goRbUTatu4uCFg7zW+xo7l+6MaYxwWI58FwBvzX0Jj5FMBEHAbDazcuXKSWVYhoaG6O7uRpZlsrOzA5tPqg+hXloUnh2fIO2JD2BqfgItd/cVmzSQSAmaeMcN/RISKkAPPvggw8PDuN1uWltbKS8vj/u9O3/+PHfeeSe9vb2IosiHPvQhPvGJuSnjZAhOkpgu3VnPOIsnrVEXD03TOHPmDP39/WzZsmXabzqJCs7h4cMAXLfiupjuicWl1tvby+nTp9m4cSNutzvQ4TCR8Xct20W2JZtnzz6bsOAIo93+yshV701p2+iZEFoJWVGUQDfM8+fPo2ka2dnZgQB0qtJklVX7/bGco99Fu3YHgpTcsviLOYYTK9P1cAoWoO9///s8++yzfO1rX+Pzn/88bW1tXH311TzyyCMxz2Uymfj617/Otm3bGBsbY/v27Vx//fVUVlYm6+XEvpZZn3GREUuDtESEQJIkvF4vr7/+OtnZ2YFqydORqEvtjZE32Ji3kaXpsbmZphMcRVECJUJqa2sxm8309/fHnWQQPL5ZMrO/ZD+/P/d7vIo35nGCsbzxCKDhrZ0f1k0sSJIUcK+B36WqV0Ho7OxEEISA9ZOdnZ08948g4K37GPYnP0Lmhf/DvebG5Ix7ifkab5mNMeNFkiTKysrYsGEDP/3pT1FVlQsXLsQ1xrJly1i2bBkAmZmZVFRU0NXVNSeCc2UmgyeJ4I58ugstUv2uWM/U6DgcDvr7+1m9ejXl5eUxffDjia0E5vE56HDyb8sdAAAgAElEQVR1sGf5npjviSRsExMTHDlyhPT0dLZs2RJwAc0kjVrn2hXXMiFPcLjvcMzjBHA7MDf8DHnD29Gyp3Y2jYdkZm3FO5bJZGLJkiWsXbuW6upqNm/eTFZWFoODgxw7doxjx47h8XhwOBwzbkYmr70RJXcN+S0/Itnh6oVijcwHwQG/a1qvMiCKIqWlpQmP1dnZyfHjx6mrq0vW8uLCsHASJFxiQCQkSYp5A9AthPHxcZYsWTLlUOR0JGLhvNb/GgD7lu+L+Z5wgtDd3U1nZ2fYkjrxCk44agpryDBncPDCQery43tYLCd+jOBz4t3+4RmtIRWZQjMZ02w2U1BQEKgCrlvEfX19tLW1YTabyc3NJS8vL/5ClKKEt/Y+7M99kvSeV2DpOxNeZyhXUpZaMkhWL5zx8XHe9a538Y1vfCOmslepYO7fzQWGbtV4PB6AiFZNMLEKwdjYGIcPHyYjIyMhczeRtOhX+19liWkJa7On720fTLAlpSgKjY2NDAwMUFtbG/aDHK/ghLPUzJKZfcv3cajrELImxzyWoPowH/8h8sp9qIWz70KYTSwWC2azmfXr11NbW0tFRQVWq5Wuri5ef/11Tpw4wblz5xgbG4utFXnFO/Dai8hp/M+krvNKrl6QCMmoFO3z+XjXu97FHXfcwTvfmbwvD/FiWDhxEGsdtFCilanRNI1z587R3d0d6MbpcrkSisfEg1t28/rg6+zM3BnXvbqw6VWpS0pKKCkpiekgZ6yEu/6aFdfw287fcmzgWMwFPZf2H0Kc6Mf91m/ENf9iwGazBfz3mqbhdrsDVbCDW3Hn5uaSlpY29e8nmRlYeyvLG77DRO+bqEu3JGVdC0UcUjVmvK/d6XTOyMLRNI177rmHiooKPvnJ+KprJJu5l+8FgJ7u3NPTw8mTJ+MSG5jewvF6vRw7dgyn00ltbW2gBHki7rF4Odp3FI/iYXPa5rjvHRgYoL6+nqqqqkAVhUgkI4YDsGPpDtJMabzQ/UJsA2kaKy78L0pBJcrK2GNUs8VsVhrQT7UXFxezceNGamtrWb3a33Cto6ODI0eO0NTURHd3Ny6XK3DfxdKbUM3pWN74ftLWkqpT86kq3pnsMWe72+cf//hHHnvsMQ4ePMiWLVvYsmULTz/9dMLjzQTDwomC7kLT6x8l8g0lUgxHL2C5bt26QDFIndkQnENdh0gzpbHWFrs7TZZlBgcHsVqt1NbWxpSamyzBsUpWdi/bzaHuQ3x666eRhOk3A6nz/0hznse175swT09qz9UJckG43Iq7pKRkUhHK4FbcXq/GyJq3k9P2OMLez6NlLkva/POdVJzDSUTEJiYmZtQLZ/fu3fOmjJJh4UyDqqp4PB4URUEQhLgqOAcTmqWmd+Ps7Oxk+/btU8QG4ks0SARN03il5xXqiuqQiO0BGB0d5ciRI6SlpVFaWhrzOZBkCQ7A3uV7cXgdNA81Rx3HcuyHeCy5yOunr369WJjJpqKXYCktLeWqq66iurqa5cuXI8syLZl7QVUZO/gg/f39eL2JpaYvNObLYVK9/M1iwBCcMERKDJiJ4OjioacOWyyWQMOxcCSSABAPnaOd9Ln62LF0R9R59BhTU1MTmzdvJjs7O+4kgJmcwwlmx9IdSILEK72vTD/GcAemzhfoWnYDSLNfImahozciy8zMZMXm3chrb6Dw/NM4Ry7S2NjI0aNHaWtrY2BgIGLNv4XOfCmXs1jaS4PhUptCtIoBiYiAJEnIssyFCxc4d+4cGzduDJwmj0SqXQ6v9frToXcs28HZgbMRr/P5fDQ1NWE2m6mtrUWSJAYGBpImIPFen2XJYlPeJl7pfYUPb4yc5mx581E00Uz3srdQEPPM0Um2ayKZf+dUnuD3bf8L0tqfYZ3zDXzb3j9tK+7s7OxF0Sxsvlg4i6W9NBiCEyC0YkCkts+JWDiaptHV1RWoGDAfHsbDfYcpzSxlecZyzhJecEZGRmhqaqKsrCxwUhmSKyDxXi8IAjuX7uShpocidwL1TmBuehy5/Ca8ltyY541lXckk2eKVSsFRltegFG3GfOwH+DbfMW0r7jNnziAIQiADbqG24k6V4FzJFo7hUuNyg7TgigHhSMSlNjw8TEdHB+np6VRVVc2K2ETbyHyKjzf636CuKPwBSk3T6OzspKWlhS1btkwSG4i/okGyBUqvpxbJrWZu+TWCZxTvlg/GPKdBeAIiJgh4t9yNNHQK6cJrU67TW3GvW7cuUAVBb8V97Ngxjh8/zpkzZxgZGZk3AexozJdU65mmRc8nrnjBURQl0LgsWrpzPLEIvbNlW1sba9asmbVvKLGssf5iPS7ZRd3SqYLj9Xo5fvw4LpeL2trasOuON76UjEoDwazKXMWytGXhBUfTML/5nyiFVajF25M250Ig1UUx5fVvQ7NmYz7xWNT7zGYzhYWFrF+/npqaGiorK7Hb7fT09OB0Ojlx4gRnz55ldHR0xp+NVAnYfBEcoz3BIiBSK4HpiPVh1jtbLlmyhJqaGoaHhxkfH5/pkmNCF5zpzPbXel9DEiSqC6sn/Xx4eJjm5mbWrl1LUVFRxPtTLTjRrhcEgV1Ld/Hk2SfxKB6sQdWMpa7DSIOtuN7ywLxNhV5ITBIxsx3fxlsxv/kjhIkBtPTYo2PBrbjHxsYoLy/H4XBw4cKFGbfiTmWDsmSPm4hLbaZp0fOJK1JwVFVlYGCArKysuA9xRkMvy19ZWRmo8pvqFOdgYrFwDvcepmpJFRkW/4dY0zQ6OjoYGBhg27ZtgUKB080RT2ZSMgVnfHzcX5EhczO/VH7J8YHjk6oOmOt/imbJRN7w9pjnmyuSbZHMRtl/71UfwHLs+5gbf463Lno78kjE04o7WhvmVJTKSRWJZKkZFs4CJTgxoLm5mZ07E2/mFYosy7S0tKAoSqAsv06iyQYQ/yYSLb4y6h2lZaiFP9/45wB4PB5cLhc+n4+ampqYLb25iOH09PRw5swZiouLKXAUICHx26bfUuwtJi8vj3RJxnTqt/g2vhfM04umQWyEfv60vDXIK3Zirv8J3pqPghjf5hnu7yoI07fidrlcZGZmBvoAhX4hmi81z2Ih3r5YsLhiOFeM4OiJAakwv/VsrtLSUpYvX56Ufjhw2TKK5xtRtLneHHgTDY3qomqGhoZoaWkJFHyMlUSKcc7EBaeqaqAFc01NDaqqUlxczJaLW+hwd2Aymejs7CS3/VdskD10L72ONJcrsDGlqpTKfGO2Gpv5rroT+1MfQep8AWX1tTMeL5RwXTDDVUHQLaCFZOEoioLVGl9DO1mW56TdeCq4IgRHj9XE0kogFvRx9Gyuvr4+rrrqqojfQmZaoSCZgnOs/xhm0YzdYafd0c727ds5duxY3OuarRiOy+XixIkTLF26lIqKCoDASfeawhoebnoYa56VquIq0o5/Ct+SCiay1nLh0sbk8Xjo7+8nLy8vKS2a53OG1WzVKJPX3oCaXojlxKO44hScRL7w6VUQ9EoIeituPebo9XpRFIX+/v7Za8WdIIlYY4vpy9KiFpzpEgP0wHe8f3zdZeX1emloaCAzMzNqN85ELZxEO3hOd88bfW+w0rISs2Cmuro6sO54NqvZcqkNDAzQ1tbGxo0bycnJCaxTp7awloebHuZo/1Fusi5H6m/Ed82XKS0tDWxMR44cYXx8nAsXLkw6nJiTkxO3L302rIf5Rtg1SmZ8G9+D5ehDCGM9cdVXS4Y1EtyKe9WqVYyNjdHe3s74+Djnz59HVdVJf+dEjiLMl8w3TdPm9ZeceFm0ghOtQZpudSQiOH19fXR0dLB+/Xry8/Oj3pOMkjjJuOdc7zlaHa3cVnYb69atC/xc3+Bj3fxSfQ5HDyKfPXuWmpqaiO6E8pxysi3ZHO0/ytsdL6GZrPgqbpm0TpPJRFlZGaIoTjqc2NHRETi8mJubS2Zm5oJxy0QiVWX/w43pq3oP1iPfwdz8K7x1H4t5vFSJrM1mC1S/TkYr7lStM5EsNVg8Vs6iFRxZ9jfpinaIMx7zW1EUXC4XFy5cmHYjDGU2LZxw9+hngl7peQUVlZ0rJydLJGKBxOtSixWPx0N9fT2CILB9+/bpz0UJItUF1RztO4LpzGnkdTeBLSfi3PrhRP1LgsfjYXh4mO7ubsbGxrDZbAEBCtsfZp4zWzEcAC13NfLyOsxNv8Bbe1/MKeipCPCHWk16K269W67P58PhcDA4OMjp06eRJClg/WRnZ4ddT6oSEeKNyS4m6wYWseBE+xYer9WhNxszmUxUVlbGFcRL9OBjMgRHPxOUn5/PeM44Uq/EVflXhb0n1gch2Qc5dfQkhvXr19PW1hbT5llTWMMfuv5Ah+qieNP7wl4Taa3BZ0OCU3M7OjpwOp2BwHReXl7cgd7FRKS/g6/qvdif+yRS11GUktqYxppNK0wnXCtuh8NBf38/p06dCrTiDrZ0UyU48XpVPB5PxAK/C5FFKzjRiFVwNE3j/PnzXLhwgU2bNnHmzJmUd+LUmang6A9URUUFeXl5HPv9MSrzKrGb7FPuSWXWWTQ0TePMmTMMDAwEKmi3tbXFdO/mHH/zuOfMmZRfENi+1DfJao0nLhWamhscmJZlmfT0dDweD7IsJ6VE0UKqpRYOufxmtIN/j6npF3MuOPFs4haLhcLCwkBbkFBL12q1kpmZiaqqSV9vvBbOxMTEojmDA4bgTHuN1+ulsbERq9VKXV0dkiQlHI9JhEQFR5ZlTp48ycTERMD155bdNA81c3v57VPumctSNT6fj4aGBtLS0mI+B6TT2dnJPXfezsp7PBw87+Zjn72BjPR0du/Zw/79+zlw4EDCQVdBEMjKyiIrK4uVK1eiKAoDAwOMjo5y4sQJAHJycsjLy4volol1nvnMtO+dJR3f+rdhbn0Sz4F/BEv0syKpOJYwU2sk2NIFv1egr68Pl8sV6P80bSvuOIjXwllMhTthEQtOtA9FNOG4ePEiJ0+enFLmZTY6ceokIm6yLNPe3s6KFStYv3594H1ovNiIrMpsK9w25Z5UpzlHYmRkhMbGRtasWRN42GPl2Wef5UMf+hCqz8fHez9MXd063pbRyqETjbx44gTPPvssAEvycrn2uus5cOAABw4coLi4OKG1SpJEdnY26enpbNq0KRAXGBgYoL29HZPJFKienJGRMSdCMtsWDoC88b1YGn+Bqe0p5Kr3xjReKmI4yXzddrud/Px8nE4nFRUVOJ3OSa7WjIyMgADZbLa4y/DEKziL5dAnLGLBiUakcjN6gH1kZCRsg7T5bOH09vbS3d1NSUkJZWVlk35XP1gPwOb8zVPui9fCmano6m7Krq4utmzZEtcDpSgKX/7yl/m3f/s3Nq0p4wef/kvKlvm/EPzJ1TX8ydU1AJzvH+BQfRPPvfY6f3juWR5//HEAyteu5cC113LgwAF27doVtS9RuLXD1LiAx+NhaGiI8+fPMzY2RlpaWiABIVpplmSRqgDzdGtXlteg5pZhbnw8ZsGZbxZOpDElSUIQIrfiPnXq1KQqCLoAJXOthoWzSNCbogXjdDppaGigoKCA6urqsA/GfBQcRVFobW3F4/GwatWqsPGF+ov1rMpaRZYlK+w8qUxzDkaWZZqbmxFFMdDQLVYGBga46667OHjwIHdcv5+v/sVd2K3hkzdWFBZwx3X72b9lE0U5WZw8333J+mnksf/6Lx555BEkSWL7li3svyRA0TIPp9sorVYry5YtC9QGczqdDA0N0d7ejtvtnpSAkMpT47NuWQkCvspbsf7xawijF9CySqa9fL5UYI5GJNdXuEOougDp1TCysrICAhTubx3P38iI4SwSQi2c7u5uOjs7qaysDBwyjOW+WEnkoGksgjMxMUF9fT3FxcVUVFTQ1dU1RRA1TaNhsIF9y/clPE8wiQqOnum3YsUKSkqm35hCOXz4MLfffjuDAwN8468/yvvfeh2azwvTiL9gs2OSfQiCSFXZSqrKVvLRW27G4/Pxems7h040cuhEIw888ABf+9rXSLPb2LVjB/uvvY4D11xDZWVlQhtZ8LfiFStWTDoZ39jYiKIogQOJybRK5uogqa/iFqx//Brmlv+JeiZnIVk4sYypt+LWY32qqjI6Osrw8HDgWczOzg6kYceL4VJbIET7UOvBdVmWaWpqQhCEmLpxJlqIM5FUy2hCoItkVVUVWVlZgXtCKzmfGzvHiHckrDsNUl8bDfzJAfX19WzatInMzMyY79M0jYcffpjPfOYzLC8q5LkHvkRV2UrwuhEAwWxGM5lBUy8JkAqC6P+52wVhPgZWs5ldVRXsqqrgb+96H6PjE/zxRAMvnmji0IlGPv9/LwBQkJfLvl272H/99Ry49rqA+yxeQk/GK4qCw+Ggu7ubkZERxsbGAgkIWVlZC+4AqpZdilxcg6nliahnclIVZ5ovVpMoiuTk5JCTk0NZWdmUVtwTExO0t7fH3Ip7MVWKhkUsONGQJImRkREOHz5MWVlZzMFkSZLiKs2vk2jGWThxUxRlUmXq4A9tuHkaLjYAsCl/U1LWFo9A6YU3fT4fu3btiiudeHx8nI9+9KM8/vjj3LB3Nw/f90FyMjMmvSeaIoPid40KADa7f8NTVQhsGBHaVVusaLKPLJuVG+uqubHO3x+oe/Aih+r94vPiyy/zyyefAmB1yXK2bqri7e96F3uve0ugvXK8SJIUOJSYlpbGihUrcDgc9Pb20tbWhtVqDbjf4ukNM5elcuTKd2L7/d8iDjSjFm6MeF2qrJFkd9JN1jpDW3EfOXKEnJycKa249UOooS5mvVXDYuGKFBy9TtfQ0FDErpaRkCQJj8cT95yJxH7CWSu6W6qkpISSkpKYKlPXD9aTYc6gLGtyIkHwPamwcIILb9rt9rg2hXPnznHffffR2trKFz72YT7x1v3RNwCTGUGV0eQgATJbwJaGIIpo8iULCL+7TXO7wg5TnL+E267Zy23X7EUD2nr6eeHoG7z4ZgPPHHyBXz3zHKIosGV9Oft3Xs3+a66lbt9+7FnxJSDohJ4LCe0NE5wVFa1X0VwJjq/8T7Ae/AfMzU/gmUZwFptLLR701x5c7SJSFQQ9BduwcBYIkT7UbrebhoYGLBYLRUVFcf8xZ+pSi4fgeJGmaXR1dXHu3Llp3VKRLJyqJVWIQvgHKBXncEILb3Z3d8c8/q9+9Svuvfde0tPTeeI7X2ffqhisT92tFvK3ERUZPC4wmfwCZLGA2ewXHkmaNgaEJCEIIuuXFrD+bW/lnhuvo7e/nwuOMb/1U9/EN//zUR78wX9ht1qoq6pk/45a9u8/wObqWqTsXIRpRDbSe6g3JysuLg70hhkaGgqU5s/KygpkwAUfcp3TMij2XOSyazC1/g+evX8XsU/OlSw44cYMl+3ocDg4d+4cH/zgB7Hb7WzYsIG6ujq2bt0adx22P/uzP+Opp56isLCQxsbGpL2WRFm0ghOOvr4+2tvbqaioQBRFurq64h4j0Sy1RC0cVVUDmV2xxJlCxWDCN8HpkdMcKDkQdZ5YmU5w9LTy0dHRKVlf0TYbn8/H5z//eb71rW9RWVHBEw/+M0tFxW+lCCIoPtQw1qVgtqCpSnjxCJlPkExoTqf/v8EvVPr7qcj+OBCCPwakqCB7J41lliR2VK5nR+V6PvO+dzHqdPJa2xlefP0Yh040cv93/x2+++/kZWawZ/NG9tVWs3/PHso2bEDIzEXIyEII2jTi6Q2jZ0WNjo4GUrCDK2Anu3ttvMgV78B8+ndIF15DKd0V9ppUWg7JZK7cdFarlaKiIoqKinjjjTf4whe+gNfr5Tvf+Q7Hjh3jk5/8JHfffXfMc95999187GMf484775zh6pPDFSE4iqJMauBlsVgYGxtLWDhmsxCnftp55cqVLF++PO55mi42oWoqm5eETxiA5LUb0Atv5ubmTim8Ga0idVdXF+9///t59dVXuffee/nAru0sFWR/+MV7WWREsxlNFEEDTZYRBBFN8fljNtOvGsFqnepGC4oBgV+QsNhAVREEBVVTESKMrSGQlZvH9VfZuf6qSgD6hhz++E99Iy+eaOJ//3gY/t93WbW0iD2bK9m3uYo9O2rIX16KoGiImoAm+xBMsRWRDQ5KA5MqYF+8eBFFUbBYLHNSAVtefR2aJQNz8xMRBWchWTiJVHWejkQrRd98883cdNNNgbYo8bB37146OzvjnjNVLHrBGR0dpbGxMZCKq3/YZ9oULdX36XGmwcFBamtrycjIiHmeYMHREwY2LonsV0/EwgkluPBmuJYN04naCy+8wJ133snExASPPvoo79haSedrh4CpMRFNVeBSXMtv2agIVhtoGprsg5CzVeAXBixWNLc7+oszmdHcTri0Vj0OJEgSgqygShIaIIgSgiRNEbCivBxu3b+LW/fvQtM02rt6ONTcxotvHOd/Xn6Nx373fwiCwKaylVxdWU5d+Vqyu06TlpOLkJ2LaM9AyMxCyMhCtEcPFgdXwM7Pz6evrw+bzTY3FbDNduR1N2JqfwbkfwbT1IKn87G0zXwe0+VyBZIGBEFY8EVkF7XgdHZ20tPTw+bNm6ds2LPpGtPvi3VT9/l8NDU1oWkaBQUFMYsNTBWPlqEWSjNLybRETkWeSeWAcIU3wxFOcDRN4+tf/zpf+MIXWLduHc899xzrbALy2VPRJzabQZH91kdwlprZDJIJ8FsOCPjdZp4YxMZqQ/O4pia1yT7/WIqMqCp+oRNFvwvLavdbWGGEThAE1q1Zw7rlxdxz/X5kReHN9jOXrJ9GfvjMH3jkqd9hNZuprdzA3k0V7N1UyaaylUiSiGAy+4UnIwshMxsxIwvSsxAjtNTQNA2TyTSnFbB969+Guem/kc6+hLLmurBrXCgutVQcJo3XwjEqDSwQVFVFVVXq6urCfnBmQziCiXVTHxkZoampibKyMjIyMjhz5syM5mkZbmFrwdZp70n0IGc8hTdD53A4HPzFX/wFTz75JO9+97v53ve+h324D7mjJXCNhoYQ7iCNyeSP14R7P5WgWI4AqtnqT4+22ECW0Xye8GNabRGz1oJRRQk0FcFz2bUxORYkgKaiyrI/YSBoTJMkUb1+LdXr1/LJW29hYOgirzSe5I2zFzh07ARf+fHjfAXIyUhnd1UFezdvZO/mjaxaWujfUM1WUBQEiwUhPRMxPfOSIGUipE+tIBFLBWz9UGJubm5SYhZK6W40WzbmticjCs5CEYf5YOEYadELBEmSWLNmTcSNdLZdatHm0zSNs2fP0tvby5YtW0hLS2NiYmJG7Qkuui/S5+yjIq8i6j3xviZFUThy5EjMhTeDBae+vp7bbruNc+fO8cADD3Dfffeh9nch95xFsKcF0pr9vquQgSQTmm7ZTIOG/5yNSfEh+NwIXEqH1i0gQUS7lCQgWGITG81kBlULa80Ex4I0UUSUTP7/t9n8c6kqyL5JiQ3pNht7tm/lT/dcDe+/lX7HCC83NHOovplD9Y089drrAKwoyGfvlk3sqapgd1UFBdlZaC4n6mDf5PWpGhbRhFd2IaZnXBKlDL/LkfAVsPUEhHPnzgFJqIAtWfCtfSvmtqdBdoNpssW7UARnvlg4wS61xcCiFZxoJPqhT0W7aL0Ngt1up7a2NvBBTzTRQN/YW4b81kJlbmXUe0LrykVCL7zpdrvZuXNnzA+DLjiPPvooH//4x8nLy+N3v/sdO3fuRHUMorQ3gnZJFPALg2D3xxw0n9e/yYv+Yor+TXua0+xoCFZ7eDeaqoLqDcyDPQ1BURDsaaBpqBHiQILZDB4PohZF6ATRnwmnJzqEjCWYJH+cSBBQFQ3GR0GzgQCFOdm8c8/VvHPP1X5XZU+fPwGh6SRPvXKYnzz/fwBsXFXK3k2V7N28kbqK9aTbrIHXJjoGkFVfyJxmhIxMhLSMS1ZRJoItHTH98vkeuHwmpL+/P1AB2+PxMDY2FlcFbHn927A0/gKp8xDK2rdM+l2qxGGxithMS9u8733v44UXXmBwcJCSkhK+9KUvcc899yQ83ky5YgUnURKNd0RyxenujdA2CNPdE+v6WoZaEBBYn7t+2ntiPYcTXHgzLS0trgfB6/Xy8Y9/nB/96Efs27ePxx57jMLCQjTnOPLJY2ghG7mIBl43iCICoNlsCKLJnzQgy1FqqKUFubIEInoLLVaEEMtGBLD4rSANwZ8qDWg+OWomnCZKCKJ0WWzCXaO7As1WRI8TUVP9adIms/9ckKb6fy/7WL1sKWvKyrj7hmtRFJX6M52XMuCa+cEzv+d7Tz6L2SRRU76OPVuvorZsBeXFRVPnlH1ojiFwDKFYbKhuVyApQrTaLglRBkJaBrnpGeQVFSCsLsPtk3nzzTfjroCtrNiFZsvxu9VCBGexl7aZjkRjODMRnJ/97GcJ35sKFrXgpKIV8ky6dwZXDQgOtm/bti3sCfJEXF3B4tE81ExZVhlp5umDjrGIaGjhzVdeeSXmNZ05c4Z7772X1tZWPv3pT/PFL37RX7jS68HX/PplF1oIwR41URTRvC4ETfOLkdXq36BVDdXnRdDfJ5ttUtwkIhbrpHTrSVyKAwViM4oCFjOCyYRqtoDZ4nfFBa9VFP3VDHxRqlDosRiP+9KeL/g3f58XQiom6VaXYEvDhMa2ig1sWbeGT7zzbTg9Ho6ePMWh+iZebGjhX3/yCwAy7TZ2V1WyZ1MlezdXsmbZ0sufWasd1TkxaQ7V4waPG2V48PIPrXY0pxPNZCL34hCr1lcgpKfhETVG+3s5ff4cLg0yL53/mVIBWzLjW3cj5pO/AZ8LzJc/24vZGknFmD6fL6XVxWebRS0484ngTd3r9VJfX09mZua0wfaZtphuGWqhbmld1HuiCXNPTw9nzpyJu/Am+BulffCDH8Tn8/HjH/+Yd7/73YA/vVluOeZPQY6wpkBqstWGprvH9M3qUtYYgCgAViua2YIgy2gmU8CV5b885KFIQDgAACAASURBVLWZLX6xifZlRDL5Yy+qAqqCoChIqoygXkoIMJlBEFA1zZ+WHVXoLovNdGhw6czQ1PdGF8F0q419O2rZt6OWv/f5uHhxiIOvH+NQQzOvtbbzzNFjABQvyWVP1Ub2btvCrvLVFOZMU35H81uHuihpXi+ScwK5139AWgRygGwBMFtxd5/BpWqckhUUk5n0JUvIzC8ku6gIsfQ6LA0/w9T5IvK6t16eYoFYI/PFwgEWXDHX6bjiBWe2Ch7qsR/9vEp5eXnU6sOJWGh6DGfANcCgezBqwoB+T6RmdPqB2VgqaQejN0r76le/yubNm/niF7/Ivn3+9giapqG01aOODU87hj/wHyQ2OkFiFECSENxBFQQsFpBMqBYrmsl8OePNbPaLVZT3VRMl/zhKiPWl36ep4POAKCCKZr+Foick6HE0Wa9c4F+zYLZMfS3hXrPVFlGIAVB8/sQJi9XvHgOWZGVw09U1XFdXTV7eEjr7+jh0vJ5Dx+v53Rtv8osXXwZgw4rl7KmqZE9VBTsqysnQLWsBBMtkC0hDm1r4WRQRJDOqy4VVFLGKkGOS0DQNd28XzjPtDLndaKLINsGO/PvvMHJGRUpLQ7TZ4eIQyngRPrcTwWZHsNkQbXaEGWyqCykRIZ5naE5LFaWIK1pwdBFIdgmLcAiCwNDQEA6HY9rzKqH3JErzUDMAlXnTJwzo84QKTnDhzYqKirBrifSgDw4Octddd/GHP/yBO++8k29+85ucOnUq8ABp3WdgbAjRnoamqn43lDr54fKnAVvQvLEd1iS0gvclq8SkKoiaimi2+y0gTUMTBDSvFyHCA60Junss2qluASTLZddcaEICIJhMfsETRVA1BLMFVfaFnXs6yyZ03mCxCfxUVRF9PjSPi5U5WXzgmj3cecO1yC4XTee7ONTQzEsnGnnsDy/wH888j0mS2LZ2NXs2bWTPls1sKSnGHPws6C4/HUlCQwxryQmCEKgBJ5gt+DweHH3bUXxeLrQ0IUkmbHYbqseLPNDDuM3mt6YmJvxiZ7b440k2G6LNhmC99G+bzf87mw3BakW0WBGs1kkCtVCspkQsnLmsAJ4KFrXgxNITZyYHHmP9ILjdbtra2gAmZaGlkpahFkRBpDynPOq1odWi9cKblZWVgQymUCKVqjly5Ai33347AwMDfO973+ODH/zgpOtVxyDqhXb/fIrsz0iTRH+gXhDRFBXN5/af6Pd5/XGa6RfvtzaiZI+BhqDIIPsuz2ky++9XNTSf30WnCQKYTNMG/i+9A/44UDSLRbsUs3BdFhFR8FtamiyjSRJYbaiyD1EyxeSWCyc2/rmCROySRaW63YiCwKbSEjaVlnDfzW/B7fVxtPUUhxqaeKmxhQd/9b98/Zf/Q7rNxs6qCvZsqmLPpkrK8pdctnBM5stfDqZbncWK6vEiahrOwj8FoBiQfTIutwuPx4NnwIM5Mws7I9hsdsxm//uteD0wNhI0mAiSOexrFSyWgPiIPb2MOF2XfmYJ+rd50s8EsxnBbI54cDb0vVwIIrbQWNSCEw2TyZRQinO0umDBDA4O0trayooVKxgZGZm1D1zzUDOrs1ZjM0W3pHThna7wZiih7j5N0/j3f/93PvWpT1FcXMwLL7zA1q1bJ1/vcaGea57qKtDwu7nQqwVY/am8Vpu/VlrQJufz+RgcGMBkMmFPS8eWkeEXkmnQ8KcGTxER+bJVJAigmc0IpktWkEXwtzOI8IVEiPGgqGC1o7lCLRYNZB+iz4sky+DzIFltaF4Pos2GJvjdef4N3geq/voii83l1yFMEptw2Cxm9myqZM9VVYDIxaEhXmk+yUuNLbzU2Mzzrx8H/GnaNWtX85ar69i1sZLi/CVoFovfGlX9lbk1Rb4ca7PZUZyusOJvMpvINGficbvJLCgClxOXy8XQxYvIiozVasVut2Oz2ZEkMZAlGOk91rxeFK8XQVYQenpxR6iEDlz60iKhuNyB90gwmyYJkGA2+/9Wsuq3Ss904HD7/1swm/z/Nkn+2J0m+EsdSSKY/CWOBFH0/78kIdmsSBlTE3XitXC8Xu+iShiAK1xwZnqIczrx0DfvkZERqqur8fl8DA9PH7NIFpqm0TLUwu7i3TFdr5/DeeONN8IW3gxHsOBMTExw33338fOf/5wbb7yRH/zgB1OakwmahnimCU2N3rxOkCRMmoLg8wQ2BUxmxsbHGRwYID87G1VRmPD5GD53FlEUA+4ci8UypUK0ZrLEYLHoZ238G5wACKIAZtuldGUN1ev1p0pbI/fSmYTVFkZswsxruyxK2qXijLokBzLlJAlEk7+oqPVS1QTZN/W1wrRic3lSEU2Q0DwecjMyuLm2mptr/Q3ozg8M8nJTC4fqG3mpqYXfXhKgdcXL2L2xwh//2VBOVloagij4zx1ZrOCTEdPsfrHUdFFS/VmImgoIKGYLuJxYLBYsFgvZ2dlomobH48HlcjE6MooqiVgtNuwmE1abzW8RhsOehjw6gTBdqMNkQlOFSe+HpmloXh94g75wWNOQHZerx2vdXYy5Jn+REW025FH3lBYYwUjpaRTddnNYwYnXwnE6nVH7Hy00FrXgRNs0Z1pPzRzBNHe5XDQ0NLBkyRKqq6sDMZJE3Xfx4lAcDHuG2ZC7IabrR0dHGRwcZMuWLWELb4ZDt4ra2tq47bbbaGlp4f777+czn/lM2IcqfagLNI8/bXka9Iy0SX85TWW4rwe3203p8mL/Zmm2kKFqaEuWILtduJxORkZGAt8KdQFSTRYErzv6vBZr+IC+4vP/Awiqgma1IqCB3b+haLKMJnunbnqW2MRGMVujX6deatHg9gf0A/Eh86VyOpd6z2heGU3VUD1RYk+CiCb6xSYcKwryed/+Pdy6bzcDff0Mudy81NTCS00t/OzFl/nP5w8iiSJbVpf5S/Bs2cKWkmIspkvrCJ6KS9ajJCFYbDA0jJie7neH4TeONE3FbrNjy8hEE0RUjwfX+DjOS3XgRFHEZrNhs9uxWix+C8WWjjw6Nv3rNFnQZAU1SoVlv9iMT3uNaLMjjzj9WYuRpsvKoOi2mzHn5YT9fbwWzmIrawOLXHCikYp6av39/Zw6dYqKiopJ3/ITtaYSodvnb3YW7cCnfhaor6+PnJycmMUG/GL+61//mvvuuw+bzcZTTz3FtddeG/Zatb8L69hFtCgPT+imr2kaqqrS19eH1WJh2aU24Ipo8osI/g3NbLNiTk8nSxDRFAXP+Dgu5wS9Qw4U5wTYbWSoKjabLXw2lNkScfMNRjNbEX3eST1y/PEgyb/xC/7NRNU0NJdrmloIl94XswXROQH26YtoClZ7+EQCTfVnx3Fp40ZD9DgR/j97bx5sx1Xd/3723j2d4Y6Sr3WvrixbHmTJA/IgMRgT4x8xQwIOyfv9YgIVSIAMBCqVh5OQSkiovEB+IakUL4E8XmUglYcxFX4vYAgQMHmGwjZgDAFLlmTLMpJlSVe683TG7t7vj93dZz7d90oCW9aq0nTVvXt3nz577bXWd32/nnFEIkLMmc5VjQ4CwiAwDiftfm2LsFxBCdi5dQs7t27h1193B9V6ne8/9TQPRg7ob+/7Iv/n5/6dnOPwkquv4uU7r+bWa3Zw9eTmZMOnhUDYLuHqKqJWhYqJEtp9tEHx1ZBCUBgeoihHQUr8IKBcKrNcKTOzsoqybLzVKjnPxbEsUwdrQy4K2yGo+aZht+eDBWFncDa5HP7CKjrsHUrZI0Nc/KafxRrsTbS71gjnfFP7hAsO56zxqcW7/dXV1a71j/WSfsbR0Vpe1GdrzwJwxfAVPY9pJt68/vrreeKJJzKPX6/X+ehHP8qnP/1pXvziF/PJT36SLVu2dD02LC0TTh0xcOF+ME9lmRRRbEJQq9eZP3WKkdHRxk5PWS21F8CM21QD8goe7tAww2hOn5zCFg3Z5o70W9Kzk96TI9qRcI0JRNevg+UYp6QEWC5aKjOrMGyVT3A8WFlOdUo9nU3HcR5icbGRYguCrqkfabvoeh2Z8xqRUZz+8n1Tk1Gm2VX7fsf8XNvmpTu289Id2/m9N7+J+ZkZvnXgCR7cf4AHHz/A//GYUZXcODjALTuv5uU7d3DrDbsYzzeUa7tlHoyDqDfmHIZooj4roGApCsUibLyI6twC5UqZhcV56vU6gR+wsrJMPl9AOTbCdQnKdaTjGHi8EMa5mNjUmA7RWhGW6yYNqLVJtUXPAilBgMzlqc+t9H13nYtGufgXu6fRmu1ChHPB4ZyVCKdUKrF3717GxsbYvn171y/UmUpTr8XhnKifYKIwQdHuvttaXFxk3759CfFmtVrN7AxPnDjBW97yFh5++GF+7dd+jb/6q7/qWdjUYYA+sh/h11CWQrseMl8wxfBazaSKwBS5hTAKm5H59Tpzs7Ns2rQJOx5fCBOhZJirCAPw69giJJ/P4+U3opXErweUVpZZXFqiWqthOx551yaXy/WEx2shTcos7bpSmb6deHHyfQRN4m5g0Hi2azrunRxa1CKkXOfYWUlFcXKE5dX+fRtat9SedNj5LsYcdloIkLaBrddqyFzBUA8FfkLNI9wcYbnEUD7Ha27axWtu2gXAidk5Htx/MHJAB7nv298F/oVtF1/MLTuv5trxTdyx+2ZGB5saiC3LOJsUPj/h5QmWV7BtG9u2GRwYTKTXgyBg+vQpAiGxpYVnO+RyXtfvjUYg7BxBEyKu+cmZx6hR+QK1hWWEEgghEydknLpASIE9OsxFb7wDlU+vtVyIcM5zh3OuajjNzmNqaorDhw9zzTXXJCqMveaynkau9UC3j9ePs+OizobPmHjz+PHj7Nq1q0XYKcvcvvGNb/DLv/zLLC8v86d/+qf81m/9Vl8UjX72KWhqxoydgABDYqncqFNfJLt4rTWzs7P4QcDFF1/ccDb0qbO0m9VMWxNxqYUBIgywgaFigcFiAW271CoVSqurnJ6fh1od14vRUmax0oBQNrqedl1hYLx+/3qBRkCthgh8hF9DhoEpijuOAQYIiQ7NTjusVZv35N3N8QjLq/2PIWIQSKsVRQupjmpAulZF1WpGI6hxl4h8nqBWR+ZyjYhKm89u84TL/xgb47+/4hawPQ4eOsSDBw7y4P6D/L8Pf5v/p1rlD+79V66/dKuJgK69lhsvu4w0oLLwcgTL3VNfUkqGh4YRGzdSr/pUVlYolyssLi4gELieF32m5n0TTo5gqXcaTWsNrkd9YTmqzTVFPk2mhgbYeOerMjkbWF+Ec8HhnEd2JhFOvV5n//79VKtV9uzZ0xNAENuZcLCtxeGU/TLT9WleP/T6lp83E2/u2bOn5cVPu4bWmr/+67/m/e9/P1dccQVf/vKX8X2//zkL0+iZE40fdGMHCHywHWS9CrbC1xbHT5ykmMuTa+Pc6so40M1sz5B+pphwPKiWcSW4AwVGBgpoAeWaT6lUYm5mFhmGeMUBClYFx0kRK3PcVA43EzmoJmfY1MnfpOMjlIoaVE2/iWm4jA6MU3NBYCKl9ubPbumqKBrp/0CIel6aa2jQnlMTljlGBBFku8dQIldAV8vsuGIbO668gnf+3Buo+z5fffhbHJw6xYP79vPxL3+Vj33xP/Bsm91XXsEtV2/nlquvZsfk5pZIII5sulmSorMsQl8jgiBJmcIIQRBSqVRYXV1lbm4W4RZw/fkkpdrtaylcF71SgT7ZLFXIMfbfX4dVXFvKay3rwJkSdz4X7QXvcKoZisXtFgQBTzzxBFu3bu3ZhX+2bK0O5/DiYTSaywcuT37WTry5lmssLi7yzne+k89//vP8wi/8Ah//+McZGBhg7969PaMiXasSPtNaExJ0Vkm0VIio6F0pl5menmZs40ZyuTyn/Rq4ntHHCYMELtzXLNvQzTRft8tHo20Hal2aCTXkbYv80CAMDRIoi/LSEguVKtWlFSwlCcIQv+5j2U1fHScbYaiw3dQUmZGvlg14dLOgXDwOgJczKZoILYfW6HKlg4onk7MBsD3CUme/ULNYnVCKMAwgSHkfvRzhauwgGnO3gBs2j/Pam2/kf7/zZ1mu1Pj2vsd58MABHjrwBP/z3z4HwOhAkZft3Mmt117Dy667jkkvhywYItOY204HEeQajVaSMKTrO6KUpFDIUyjkEV6Bysw85XKFpaVFatUalm1HDsrDsmyk51GbX0H2qa5Jz2Xsf3sd9kgfXrqzYOeb2iec5w7nXKTUTpw4wdTUFJdccglbt249k+llsrWCDZ6cN4wG2wa2AdmIN3ul1Pbu3ctdd93F0aNH+cu//Eve/e53J8+01zlaa/TRA52F/bYIR4Np6tR1lhYXWVlZYXx8IqmjCEAEdQhqRszMttAq+r9a3aS4mi8fMQZ0L+42XVdKA3NOyyBaNsr3KeZzFKOUSbVSYbpWZXZ5mXpgUG9uLkchLJOamXc9dDlLo6iLztBDgx8g2p6xDH2kkqaTXim0siGInFIYEPq+AS20fS+E6xGsdjqllghHCrSQvRm2m8cq9U7xabS5vmVTUD7/7UXX8d9edB0ApxYWeCgCIDx04CD//p1HANh60UZeFkU/L73qSkaKRXMLtkSHAmHZSCWhkE8aX+Mdjk7uVRJW6rjDQ7jDg5Hz0tSqVUqrq8wtLlILNLYvcVQf5VrbZuwXXoMztqHvczgbdiHCOc9sLQ4nCAIOHDhAEARceumlPxb+NVh7hHNo4RA5mWPMHWP//v2ZiDe7OeZPfvKTvOc972F4eJivfOUr3HLLLZnmpU89g+5Cytke4ZiO+RLTp6eRUjAxsbk1hRb5J2E36jHxAisJCK2GcidhYBbHrim3xpgaTJ0kLVqKL97WMW87DpZlsWnsIkNWWa9TWlnldLmEFhKvUCSfz5tUTeij63UTITjpkQ0QFfXTohFtEH390othaGoVQbkFqSYF4MRwaZOm08JwxknXjVBqzd+HKMIRmJ6WFIcpHCfS2ul/B9LLEax2OqWLh4f5+Ze+mJ9/6YvBsjh09BgPPr6fhw4+wRe++z3u/eZDCCG4Zsskt1x9NbdcvZ0XXX4lslZPGnu7XVp6OerLy13/07EEzlCRkdEh/HJIZWWVlZUVamGdkzOn8HI5cvk8Xi6Hsi02vOaVuF00h86FlUqlDo2s57tdcDgZHE6ckpqcnGRycpITJ060aNucS1sruu3JhSfZ7G5m7969bN68ec0pv0qlwnvf+17+8R//kZ/6qZ/iX/7lX7q+9N0inLC0jJ6b6l6vaT7esqmvLnNqaorBwSEGBwe7zkUrq+eOWqAb6SPbNXUbz2twowV1iHow4stmBR0Iqw9paEzjIiVeLo9n2zAyTBgElMtlVuZnqdVqWJaFl8+TKw5iKwVePhKPqycpqZZH5GQh7QScblQ5zVMTpu9FCLTf5b3ROoKfGwg3tVJCJCokxiFHrAZCCtAgCkXTle84BknWbQNkWYR1v2+vCkBoOV2dTYsphfZDLh8b4/KxMd76ytvwg4DHjh7loYNP8NDBJ/in//z/+L+/ej+OZXH95CS3XXcdL9u+nZ2Tk6jm+o/r4q+U+jpBIQWhbxyv67rRY9Js2LCBSqVCeXmZ+elprJuupa7rjCwsMDg4eM5pqi5EOOeZpTmcGHL5zDPPtKSk1lv7WU9PzVoinFCHPDn/JLvsXWzdurVrvaafHTlyhF/6pV/i+9//PnfffTcf+MAHekZGHVxqYQjHnzJpMMsyu/BYDrpWTfRttBCUlpeZmz7F2NgYrtudAUALCTqANPySsqBebUgJxEhrQDsO2vXQngeeZ2ocaeZ4Laislntu/oftJjQ4AFKZPpFCsQha4/s+pXKZ2ZlpwmqliSvMQ3qOoanxDaO1dnOp6DaIosK+9RgDQhBZnJdUEeVMO6+djnqFfES1Ym66tJLcv1BEn69RN0UINEYTSPoB2lIG9u4HHY5JeB6kpguFYaRuQwVaSnHjtm3cuG0b73ndaykJybd/8Bjf3L+fhw4e5K++8AX4whcYyud5yZVX8rLt27ll5zVMDo92MJF3PDXhtqQBYyBCMwN28UU7Kb58NwsLC0xNTfHkk0/ium6igFooFPpu7NYjPFculy84nOeTnUkNJ0Z1CSE6UlI/zp6arA4nDEMeevwhykGZ7WPb1/yifuc73+HDH/4wYRjymc98hte//vV9j++Y1/SxhHoFSJigAQP59TyCUDOzuEx9eYGJic39IaLKSi9OxxfoAV4QOkTpABH6yDBEOxEfmZTmFL8O9VoDAWZZmRBu2G5Pp2QuLLBsm8HCAIPVMlqbWkG5XGZx0fR+5HI5tNYoy0KJEC00uEbDh0gFVEfNmAR+gg5LM+2kaOmYCZpwJui/aQptG1FagnbYrw7BD9FEtTDXg1Kphf8tjpaEUgaZZ9mmhpTPoYpF03gZkYASRgwIoTapuw7wQtvs3RzuSomf2rmTl1x+Ob9x223gOHzr0CEefuIJHnriCb7ywx8CMDEywsuu3M7LrrqKl1xxFaPFYttYeepzrRQ57c2p3tZJRm57KUJKxsbGGBsbAxrNxEeOHGF1dZVisZgooLbLj6yHKfoCaOA8s14OZ2lpiX379rF161Y2b96c+bw0O1MFz15WrVZ57LHHOMYxAC4rXpb5OkEQ8MEPfpA///M/59prr+XTn/40l19+eep5zRGOLq+gp5/tfbA20gCLy6sM5jwuumybIXwMtdnZtzf8OS4y8El9PS03m4OQyvThQBIFJb7KcUxNI+nX0abbvocFUmXQyaElAhLC9IK4nsfwyAhhEFCpVFhaWqJcrlBeXU2Ykm3bTiYXL9zactFCIK1o8YlIMUO/hmjavYfKRlXLYKVsNpwM/G1KoVfT6XlEj3oMEKXvfITShHXDsqDqtZberORyUkC+QFipoPImNSqENFFy5AB01OsT1gNkzjUbjSBEKIsNQ0O8/qabeP1NNxFqODq/yIM//CHfOvQkX3nsB/yvR74NwI6Jzbz0yqt46VVXsXvHtVhznXxszQ7HHh1m4+tu70qJFEc/ExMTaK0j6PUcTzzxBNVqlaGhIUZGRhgZGSEMwzVr4VxIqT0PrV9TY/ti3twYef3111Msdu/UX6+OznocVdq1YgXR7du38/2T30cKySWFSzLNb2Zmhre97W187Wtf49WvfjX33ntv5h1VPC8dhujjh/pSf9RqVebmF8nn82zYsCGhohFmoKj2YlIxBAHUa13LQM2mY1LOFAuVY6DXTvfUnIjmom0X4VdBCYTlGiclhKm71OsR91d3MEGHKSvhOOtmUinyhQK+VOSrFXK5XLJb9v06juMmi5lU0qSu2iIqgYH8YkcRhFLocgVhuyal5td7shekwaRNxCdNZNXH4winO7qt9SCBllZXGHrLYW4Of6W110a3/V1E6TZqtQaBKT7KAmVFUZuUKCfHNtdl2/gd/PJr7iDQmsefOcpD+w/w0MEDfPKhb/JP33gA27K44dJtvGz7Dl561Q6umbwES0mk1ChHYY8MsvHOO5BeSg9WNLdisUixWOSSS8z3b2lpibm5OY4dO0YQBIni79DQUCbncyHCOc/Msiz8aHddr9d5/PHHsW27ozGy3Z4LEU5MvDk9PZ0oiD518Ckmi5PkrFwqc8B3v/td3vSmNzE9Pc3f/d3fsX379jW93Ikjn34W+nS6Ly8vs7CwwODoKCrsETmEYbI4CitKebk5tOsY2eY2gEZSG0ozZSGDmkmV9TFtu639OzpM0nkCQEmEZRFKCbaN9HIm1VWvNcFuIxNNY/QzGaPlTPptwLYZGByM0m81Q9W/tIQvFQVLkcvlcF23M00cxrUSjfKrSKkRoWN25JZqIPmEQGthkHO2Q+j7iB5zjGtFMQihqymLsFolDZImXM+oevYz2ybIABnXXdJtLekvrRG2i7+01HKMBK7btInrNm3iN25/JeUg5JGDh3j44H6+dehJPvLF+/jIF+9jwPPYc/mV3HjJVnZfehmX/487sYfX12sjpWR4eDhhH1lcXOTw4cPMzs5y+PBhLMtKop+BgYGu6bZSqdRz0/t8tRe0w4kXzcXFRR5//HEuu+wyxsfHU8/7STucZuLN3bt3Jy/r4cXDXD50ed/rtAulPfDAA9x44408/PDDa5qXEAJRLaFXpnpeZ3Z2Bt/32bz1UkpLC9RTHpmwXYiKxUqHiDAwO2zXRBxaE6XEgtR+kGjErg2nLfOUqrNnqJspC1ktG52e0Dc1Ci+alxAQgo4VQ9OQcCL6rcumwKTfXFzPZfiiMYJKmUq5bNI1s7Moy0qin4TdItbd0fEdRxZqiPWHItZoEW2wlJKmnqWU+b+4bgToWt2kPJuZEFomKY3zSvkOCC/X4Ww6NkJCoAPdl/bfjJUnWO6f/sJ28FMiLo3Asz1uufwKbrnckNvOrazwncOH+NahJ3n40JP85+N7Adj8+X/jtttuS36dCURZCEE+n+fKK68ETBp8fn6eEydOsLy8jOd5CQAhnzf9RBe41J6HlsYTVq1WOXDgALt27VpzOmmtth5HFdPoxNZOvBlbNajy7Mqz3HHJHQkart2ahdJe85rX8E//9E8tEgprkc2WQuBMPwNeZ6oqCHympk5RKOTZsHEsWgL7L/1aKZPSiq358CjiiJFnohpGejTC7PBrtc6IIoJK97ubpC8nrSYjZKKJ0zqAbgVH2E3aOyJexKPCv19v3L2VAjoAAy0PDM9aPp9P3k3f95P0W71ex8oXyKvldKEuZXeyITRFlmZedpSu0iY7ZSuwLVQulzBLA4SYBlDhOISB3xXcIWyHsJSh98h2uzActI3legQrPbjPtE5Ss2HQyXfWOVYOf7HVcY0Wi7z2RTfw2hcZhdonSyv8QIT84Ac/4Etf+hL33HMPADt37uSVr3wlt912G7fccsuaoo92HjXXddm0aRObNm1Ca23UT+fmePrpp3nwwQf5xje+werqKktLS+t2dP/xH//Bb//2bxMEAe94RzPI8wAAIABJREFUxzt43/vet65xzqad9w6nl9VqNfbt24fWmj179qwJQfKTiHB6EW/GdnTpKKEO2Ta0Dak7r3Po0CF+8Rd/kQMHDvAnf/In/P7v/34rX5XILpsN4JYXDATXy5sielRor1QMRc3GiKIG2zGw5T6O3+ykJehmZmVhutKbjxPSSAprbWSX46k6dtLIiNaRE2pOkfVwdI6bLVKymvqBet1Ds1Nqp5cRZo5CWUb4LAgQbg5UuePYxjWdrs2ilmUxMDDAwMAAWkqqlSqVlRWmT5+mXq9Tq9eSKEnEssuOm9q0aaI0k5pr/NAg/RLpBTA0PuWV5NErJcGK6kxx3UuYxV9akSRFqA09URC0sBwIL99Rt+kwpQgqld7PPX5nbRe90j91J9wc9cX+om2qkGfb7beyc2iI3/md3yEIAh577DG+/vWv8/Wvf51/+Id/4GMf+xiWZbFnzx5uu+02XvnKV3LjjTf25VPsh1ITTZuKyclJduzYwXXXXcd73/te3vWudzE3N8ctt9zCBz7wgQ4l3V4WBAG/9Vu/xf3338/k5CS7d+/mDW94Azt37sx0/rmyF6TDmZ+fZ//+/VxxxRVUKpU1wxXXq22zXtCA7/vs3bu3K/FmbE8vPg3AtsFtyOVWh/PZz36WX/u1X8N1Xb7whS/wqle9qut1skI3db2KtzpnogodICyFtm3mFxZZWlhiYmIztlKmsB/VRvqBAER7DaWHiZgrrSNYMg5IxBeSMknDhZVqRC0vWvoxdEphPzG7gYTr64qV6u+8YrZh30dEn42UgDL8XcZhYhBoWrRCzHuYkBauFeAODzM0PMzc3CxSSkM+Oj+Hkgq3WCRnVbFtqzXd1j6W3aV3R+vWM5TVHZqtaeV8s70EiZaMHx1o2RbKNf1RYbVmyC8TJxSl9SInFeoAkIigipYm7dZ+B4bZOU+Q4mywbPzVFOCClIy86pWcqJST74FSihtuuIEbbriB3/md36FcLvOd73yHr3/96zzwwAP8+Z//OR/60IcYGBjg5S9/Obfddhu3334727e3ih+uhSnasixe/vKX47ouX/3qV6lWqzz88MNrQqw98sgjXHHFFWzbZiiu7rrrLu67774LDufHac2F9htvvJFcLsfhw4fXPM6Z9uGsxWq1GsePH+fKK6/s28h5eOkwSii2Dmzl9KrZ7dbrdd7//vfzkY98hD179nDPPff0FEpb09xOH0UCQQyLDjWnp08ihGDrli2mYK0khu5YRE2N3VNqWsruwmZth7c4ry7RT3KcspPjCEIsNFJoI8cslYlEwtCMXe2vv4JUmRyhttxUFBbE9aK26AcSpmgDULAQYR1sC6RluN/iptnAOCx8H+12Ri0CgecaKWYAPwgolSsszM9Trzekt71cDku1ko92692JkWHx381fUt4Rt7Nu0zKiIS8wfHH1ep8kK8hoLCkASwKRJk30TIQwb4KsB1iDA607Am1+aXQCLJRaghP9Q+sEZk3UDzT44ptxxzcRHj7cc+OVy+WSms4HPvAB5ubm+OY3v5k4oC9/+cvs2bOHr33tay3nrbUPpzkb4Hket99+e+ZzAY4fP97yXZ+cnOQ73/nOmsY4F3beO5z4C1Or1di7dy/FYrGl0L6e7v/1skOvNTKKiTc3bNiQyhrw9OLTXDJwCbaykVJy6tQp3v72t/PQQw/xm7/5m/zFX/xFX+2arJo4enkOVhcTh1Cv1zk1dYrBwUEGh2KKGg1CIYKagQg5LgSawA+jFFuTRLNUEHZGGs1ORSONlk4yeo95Sithn+5qYYAgQFsusl5FR1EQiAiSXTeIuITIrTXN1/V5SAV+hrSc7aaDCaIFOVnUQx/R9LoYhwTayUPgI/P5qE8FdBgSWioiTDNmeXkGEAzkcmg0tVqNcqnMzPQ0YSS57RUHcMOwO/loU4pVRCJvfU1ZfVN3DSkBO0Nzp9u9v6ep7qSFIKxUkEHYt9lVuHnCUqe6aiT/AxKczZMUrr82ukT29WB0dJQ777yTO++8E4CjR48yNzfXcdxatXAac1zfWtPtu3wuWe2z2nnvcKDRq3LVVVdx0UUXtfxfnOY617xIkD0yCsOQgwcPUqvV2LFjB9PT06nnPL34NFeNXAWYcPpd73oX5XKZf/7nf+auu+7KNLc0Z6iDwDAKYF7eaq3K8sllQ1HT3KvQgfzSSEIU2vBzuU0ppF6cdE0RjrA7ZQd6n9COgmpzUEohIhoZoRt8bHHhWXseiCgSCnzA6Uk7o2OnFKag3KRKyCX7WqTR0880Bkwgmucd/WkJYZgLPBdtOUYmOqLa0WGAa7s4rsuwHibURiemVCoxv7ycSG97iU5MJP0mDPloqrMRZm790GZaQ2g76SABpQgrGZCDjmsQdf2IaV0Pv4eWTmzS9Ri85ZZkQV4PK0BsW7du7coiH4bhmgl/1yPYGNvk5CTHjh1L/v3ss88yMTGx7vHOlp33DueZZ57h+PHjSa9Ku8UOJ01A7WxYlkW9VCrx2GOPsWnTJnbs2MHS0lLqORW/wrMrz/Kara9JhNK2bNnC/fffnzlnK6VMf8Fnj5vFV8PqyiqVSoXJLZOtOzdNhNBq13BpToOZtIbQ2kRAkQMyaaMg4kYzx2urKUXWxzIdpwFijrbuJrQGocGvRn83yLgYlh3YrolW/FoHn1rPy2aIlLCsDBEQJkLswTytm1JW1CpGCjq+L4iiTds0R0qFNThM0ffR4xq/Vqe0ssLiyjK1chnXcdBa4+YL2bSI7By6jywBYNKF1fSxtLTQQcpzdXMEKyv9gS5SEZTTe4UGXvZSVBNC9UwcTi8LgiAhBs1ivu+vKyKKbffu3Rw6dIgf/ehHbN68mU9/+tN86lOfWvd4Z8vOe4czNjbG+Ph4zxdovYiz9Vga6efp06c5dOgQO3fuZGRkJDknzeEcWT6CRvP5f/o8//l//Sc/8zM/wx/+4R+uqUDYC0odm66UYPE0YRBy6vQpBILiQLHzS2H3iAjaSzjSaqSimiMNgekr8XzCMEBIC0TQUTvQzeJgfVJpIlmBMWwCWZwXImFQhkYkJLTGEiZa045r5pQvmPHD0NyD31aX6JNKM+g80fRsUhy+1dvZJHNFGABDO11Qs4WhcfCV1SSLZwsYGigwNFBAAzXfZ3Z+noVKlaVKBc/1yOfz5FzHTDeI0GtxBJTmbASEQRsIodthXi4dAKAswih119fhKBudAr7IXXElXltEci4czlrHPFNaG8uy+OhHP8qrX/1qgiDgV3/1V7nmmmvWPd7ZsvPe4eRyuYRNoJudicNZC4wYekc4YRjy1FNPsbS0xO7du1tqLVmiom/s+wYA3/r3b/GXf/mX/NIv/RKnT5/OPK+062it4fQRapUqp06fYmRkBCkl5fY+iyQN1WktEY6y+tc9tEYREkqFIKr7KFM01kFgCvTxXBvV7P43KBqptH6WhTInTjWJoK2PRQq040YQ4aiz368jlOrfJJkhUtJC9Hci0cRC24UUJvMYDdfrkQnAtSxcL8egG+LlclQrVcorSyzNVFpYlJ1cARDICG1m/KZOivKEAdoPCJVFuLDQ1+EI206lyjGicAodEY/2isqFm0tNpaniAMUX7+n4+bmKcNYSsZRKpfTeqhR73etex+te97ozGuNs23nvcNJsvQ5nrX0r0H1Rj4k3R0ZGuOmmmzrGS6v73HPPPXz4/g8z/KphPveJz/GKl7+ChYWFNaPh+oIGludYWlxgfnqG8YsvxnEcyqVyZ/FeWT3rHUI0Io2+JGnxIS0OQkeQW4PkEpaNsJyE9VnUqlEqr9uFo0VJSVKpDqRMlwnQ2jjAfjo9oQ+BNqSgOgAl0RFlj+nSN6goLVcM6CBDWk4oJ7VZNBDCNM/avcEhgAFxpFHJqKjuZDtIIRMHA2bxjKl3SvMLeOhEeqE5NZ18HJ6DKJdRjoXKOViFHDHdTmwhoEOBikldm9ikdRCiI/JVEwE1OZJu30HbTmUcQEgGX3GrUUdts/UQbabZjzvCea7aBYezToezHrBB+7WaiTc3btzY9ZxekUe1WuXuu+/m7//+77nhT29gfHCcV7z8FX3P6Wc9oy+/zvShvYT1GlsuvdQ08wGhH7YWf2VvZwM0iveWkwlqbKhY+jimeAGKnYnloYXCbPNDM5fofkLZycfWzbRQiF58b+YWCBGZxmru34GogbKZnw1QEdeZjFgTdMRMQBig6/VGGjEDM4HWUa0oRfsF20l1Njry3iIMu1LbKKUMUeXoBsJyiXq9bjrlZ2fxgwDP88h5Bp4tpDRMC4DWITIiS2036eQIyg3dneRPQbRKKYTtENTq2AXPOCshEZUS9tAAtuuB0AaeEmqkZUf3Ev3WBoXOXbkdJ5IZaLdzASL6SUQ4z0U77x3OmWjiZDlvLWCDZtaAduLNtHOa7ciRI7z5zW/me9/7HnfffTd7d+xl++j2vuekWbcaTrVa5Uff/xZjnmRk0yZMIt4coyIiS7x8kkKhFtArTyMQJj7JkNbCcpDhCmmfipZNUZDWiObCvGX6bsJaaNQ/bccsdL2cmGWbSCnFQiHTe1GEzNRUGkgLO/BbkXLxELYh3dRKQQhCFdHa9OHooIvqpush/RpC9H6XMpOeOh661J+8U0sZsXoLHMfBcRyGhobQWlOtVCiXyywsLhJYDgVB0hvU1YNZdosAWs/5hxjkXdPPRK2KqFUa0baXTwTjus1eAGpohML11/W8zvlQw3mu2nnvcNLsx0lTo5TC933+67/+q4N4M+t1vvrVr/K2t70N3/f513/9V+543R3c+r9u5Wcv+9kzmls7Sm1hYYEn9j3GtRvy5LvstERc6A5Ds7j7ddPdLwxJpGlQrLVsV0NNejpNCJOS6mOlUolaqCm6KbvGiPzTItqpJ82fUZ9NJIWAEEa3pf/M0LbTm/G62aTqTVkTj6UspF8zBf6eB4WABX4T04EkAlLIhEomRCCCgNCyzWfRw0QPupwWU6rpmB7knZi0ZrexhBB4Ebx6xLKpr65SKZdZWV6mUqmggeWlJbyIfNQEHzr1vegFJkiAF8Q1oDTwgqSw+8VGGK6HrTVVnsXWGuGsrq5ecDjno51phLMWK5VKnD59mmuvvbaFeLOfxbWVIAj40Ic+xIc+9KEWobSD8wfRaC4buiw552xwtp04cYIbLt2E06O4LxKPIxqLa5y6gCjNFeXqwxCNyLZYW3ayc+5WU5qdnaVarWG7LqcXF0x6JKovtNP3a2WhQp+geZhYiA2i6riLlpZJzSVEm53U/aZonyGVZjmponA6uXh/05bde6zmFJ2ywa9hCSNkJl0bhEo68pOMkl83TrebtDRxKq2RlusZ4ThuquPSANEiG0tvl8tlViIoc5x+swuD5ITppu+5+bJswh41mWbnoLVIjT69q67G2tA9fd1sZ9vhrCfCOd+YouGCw0m4ytZqa2ENiBfxY8eOMTQ0lNnZgHnxFxcX+bmf+znuv/9+3vKWt/A3f/M3yct4ZOkIAJcOXJqck6mnps1icELM2bb72quRM8f6nBE5BMvqvRBrnfS8SMsmdDzwCtFi6Xeep3qPFYYhU1NTeJ7HxZNb0NUyYmiQMDQNjKurq8zOzmIl9P15bJm+o9RStqDXTGOqY9JZsbMMA7OCpjI8y2xOqa2+03VekC6xDUb1NJpX3IdjPExgSEyJO+oVQgdRL45lfihV1DNlLNCYiM+JmkZ1Z4QTp9LSTDheV6i0UorBoSEGh4bQSlFaWKZcLrG4sABCJLWf1s1DH+LXyOF0gAm6mCwOkLv2+tS5nwtbTw3nQoTzPLS0nYplWdSyNLa1WVbWAN/32b9/P1JKbrjhBvbv37+m6zz66KP8+q//OgsLC3zsYx/jV3/1V1vu6ejSUaSQbBlo8CatJ8LxfZ9Dhw5x2WWXMTm5GU481fd4ISLMWDfa/nZTNsIvGwRX3HSplKHMj0k1/TqmITTa/zdFOLVajVOnTjE6OkphYJDQryV5fCllC31/XMA+PTcP9SpKKSxL9dhhatBd3o/IUYq4ihQ7Vc8jdDxErhBR4bQ5TWWlOxKZQQ4BIvnsdAeXRe5aW11g1029TwBIhfR9sxmQmOZQz0Hlc0aeABGJzZn0I7HaaxiiA79F6hrb6epsdBMZqMmuSjzPxfNciGSYy+UyqysrzEWbB3doBE8b8tFu0ZZBINoEKewFCEFh90v6shKcS1trmu581MKBF4DDSbP1EnFmSamtrKzw2GOPcckllzA5OUm9Xl9TVPT3f//33H333YyMjPDAAw9w0003dRx3ZPkI4/lxXNXoYk5r4my3mZkZTpw4weTkJFu2bEEvzWSikgkhtf0lqcm0N34CEBo8LBgNmcA3kF2t0bU6mnKiE39xBMdGyL7JKNu2sV2XwUGzGC4sLFCpVJiamkLKpv4Rx4kIQTMs/vFCGTV+ipiZWkm0ikXYpKkJuZ75s1ek01zfaWdjji+nVKrjAozD9psciaaTETqDEzTz6gKG0NowW0f3EjNKd7AXSCtBjWkp0KFEFVWjLyeMKIeCqPfHttHKQrf1yUgpKRQKyc6+HmpKi0vMl0r4vo/runi5HLmch4yjV42px6RkKdzLrsAeW7+A2tmwtTic1dVVI8d+ntkL3uGcSQ2n36IeE29ed911DAwMrOlaq6urvPvd7+bee+/l1a9+Nb/5m7/Z1dmAiXAuHby05WdZIxytNU8//TRzc3NccskluK5rEFALGZpGLRsVZnhuyvCqGW6uXt5JRItRIwISSlEONJVKjYnLr0SBSRFl2dFH6aMYQSWEYHh4mCAw4mWLi4tUajVcxyXveeRyuZ7pjmaWauhsNBRgekSEboAdIpi2ScuJBFyhtTa0/X0WHq3jqCvFkys7XcStMWj//7d7gQmaU2opjadxVKhcdK0RbTTfqdI+ttQo20LW65BzGv04kcOKL6gRKA1uscgIoIMgSZ0uzc+b2p3rUpWKsFpD9tG/kLk8+V039n8GzzG7EOE8T+1cwaJ7RUbNxJt79uxpIezLwsh86NAh7rrrLvbv388f//Ef8773vY9vf/vbXY8NdcjR5aPcfPHNLT/PspOKZaoLhQI33XQTx48fN6CBlTnTLR8E4NdaKF5arhF3kvezJjr+ZoqZDmurA4VhGDHuaibHxxurlmUbRmJtCuAi7rdpMq2snowCSlkUiwMUiwNoZVNbXTbpt9Onu4MPstZkugEFkrRcZCL6/D2v0QBaqRIqFUG2o3RWhvoOCFNXarOkhhObnUFZFGF6frpYC2jAcY2MdT/rpZeTjKdJ9Iril0d3ZzwQjocur7ZEU3lHkXcGYWSQIAioVGusLC8zPXMKy1Im+snnsZ1IfC6iDfJueLEhgM1gZ0KYeTbtQg3nPLWziVJrJ95sX/jTHMHnPvc53vnOd+I4Dp///Of56Z/+6eT/uuWAT5VOUQ2qLYCBLLa8vMzevXvZtm1bAmAQQhDWa+iy6VXRUpp+DCHNwh7UE4ZiLBtZq2T8ckbHiB5fZtGaDqnX6kydmqJQKJjnm3RJ2olzEVqbelCEhNNCIjRd+1PMI2u9ro4Yo13XxXVdhoeHk/rBysoKs7Oz2LaNUyhSdOy+LL9aiIyaOYYyR0BUzA+QOsAS0gixORZaWmauVtH8GeokPaeb0129CDybU2pSoLM02NpOh1ha84BCYHR50uDUEJGU9uHjA+ME+zglM45ApxCZKqXIDw1jn55mYmIzdb9OpVxmYW6Oer2epN+KW7fhTGxOnXtyba1/LMzxaVYuly84nOer9YsszsTh1Jt2ht2IN7Nas1Da7t27ueeee7jkkks65t/ucI4uHQXoSKn1szjVd/3117doskspseqroNvCeB2aDI9loy0HLUCGoSl+90v7qNZelJ6iaVImzYil1RKzs7OMXTyGDjXLK7EccG+ONtPwGStNOia6sSKdmFAT1uqEtVaphG5Agfb6QTUIqSwvMbO0SBB3z3fpR9LSQgQpC7tUmZpKkRLZflzE8KzjGokwfHIil28iDPU7n6yyk/6dnqbsvjoyxtoikl7muKkaNxpMNOX2p94RtpvKPK1tpwUqbVs29oDNwMCgaT6tVSlXaxyWDsGjjzI8PMzo6CjDw8N9Hcq5YBlYT9S0urp6IaV2PtqZNn72I97MYidPnuQtb3kLDz30EL/xG7/BX/zFX3TQmPeSfz6yfASArYNbU68ThiFPPvkk5XK5I9UHYOkgWjj7veQaISy00OB41G2P0M0bOpj23pX2L1m34E5aBuWmYX5hnnKpzMTmCZRSVCqVhj9TKgNDgUDEiDkdIqJzpVIIxwXPOCGtNcKvQ9g75w/g2Dbu0BBDQ0MJ9LpcLlOv15mamjLcYYUBnLDS4+aap5alJmP1lagWcX1LiQb9jgAshbYUQiq05yEKRYPEagYwBH7nohezQ/Qxrc3CnhZtIGQmCYNQWch6yliWnco8rQHt946khDDKp0O7bmbr9mvwfZ+FhQVmZmZ46qmncByH0dFRg3osFFo2cs8FlgG4kFI7b+1MIpxqtcr3vve9nsSbafbNb36Tt7zlLSwvL/OJT3yCN73pTV2P6wUCOLp0lAF7gFF3tO91YoLQDRs2sH379q7zdGor1NMWICFauMbi8q6WCpwIqRVxmSXpo56DETHlhJw+fRpLWYxPjDe6xuOISLSLufWwPsSh5nohQkcJJykNGi4p6utI1KxuivttQIEYep3L5ahUKmzcuJFSqczc3CxBtYLrOuRy+Vb0VGxWBvG4aO1PZTpQ3ceK03RKh8jQR4ZNcHUlTCQjGxLNCeGD7yNkrHYadNSFQgTC91Mnpi07tb5jmAkWTHG/1zhap3PBEfX4pEgYyEIR54qrAdP6sHHjxoSvsFKpMDc3x5EjR1hdXWVgYIDR0VFGImj2c8HhXEipPY/tXKTUSqUSJ0+e5Prrr+9JvNnLtNZ85CMf4Y/+6I/Ytm0bX/rSl/pqVfRCxB1ZOsLWwa19Hd3CwgKPP/54X4JQXVlFBTVqafQiQhELiXW9pg4j/TWJdnNJTj8GILSYZVOvlIw89dAgg4ODrf8fBwVxn04/68Py3DLLdqfUFAkhBUjHEIBqHXGYmZSVaEvnWZbFwOgoA7UqWmtqtSqlUpmlpUWABvTa9cy997K4bm47qSk3LUiny8HUiro9CxGGJDB0IRE6NHUhAUIJ82ywE0ADQhDMLyFyObNYhiGEGh36SVOoeRjdKW465hZ7uT4Lr/ByhGnUNFIRtMtidDHv+ht70td4nsfExAQTExNorVleXmZubo7HH3+cer2O1prZ2VmGh4fPCmv0euSlL1DbnKe21qgkJt48efJky64pq62srHDXXXdx33338fM///N8/OMf71xs26xnhLN8lD0Xd+p5xPN85plnOHHiBDfeeGNP5lmtNeHybCqCzoAH0hkZhLQa8OAoxaaVApWjbucI3Tz4PpWVZWanT3PR2EVdyUsbZJ8ZWJ6RjSbNrgdos4gGGTrkZdM1o5QVlhVFb4LAdtHKScYSQuC6Hq7rASOEoaHuX15eZnVmnpxlen/yubxhh+68YMYILgNljsb0FaW90pbVI02mE0AD0sIO6qigjtCRkxAglDRgjRhpJyTCtps05HQE7SZyUgGBUFAqpahzSsJyer+QlhaE/T9Ha2IS6+Lx1LHAfH6Dg2bDc+mll7KwsMCPfvQj5ubmePrpp7EsK0m/FYvFdVHerMfhXIhwLlgCJc7n81xzzTUtmuFZbN++fbzrXe/i5MmTfPjDH+Y973lPphe4GwR7tb7K6fLprvWbIOpZWFxcZPfu3f1f9vJyRLLZv6bRomfTw9pTbu2mpHFq8yurlJZXGL/sCixLmVSOX+/gL0tlZSYu2mdwSlIi/PXq4TSACZYUCNcBH3CilBygwxAR+EhfUCgUKQwMsiEIqNeqlMtlpqenCcMQL+cl2jFmXiqKPvrPPQsSLhARl5joHUVolU3KWjf93tXCEGwzVksjaNOfhppZmmfn2SjPwXJdrELeNIUKETkqQahB+YFJoyaptch5BSYaC6WFXi31lD4C07/lXbsr9f56mRCCfD7PlVdeCZh09NzcHM888wwrKysUi8XEAWWVjF5vSu0CaOAFbIuLi+zbt4/LL7+cTZs2sbq6uqZU3D333MO73/1u8vk8X/ziF7ntttsyn9stwnlm+RmgE6EWQ7Mty2LHjh19nY3WIeHKHJDSIyRVwsvVz0QqS7Lm1KnTSAGbN29uXFNIA5eNFiCTuqHTAfUYs/+kBL6QBiiQOlJ/FgPAxFGJJEIjJWeYB5T5JaQZSwfYbg6nMMBQJCtQrpQplUrMzc3ha8jX67hDQ1i21ckSkNxDI5XZ05SF9OsZKEFFKjkElmug0j2YEMwwRs001awm2LXWiVy3mUk0lLKgUmn5WWO2GKQeEXw8Zzeur0EVPOyBfMJqYF16JTK//sig3Tm4rsv4+Djj4+NorVlZWWFubo79+/fj+34L+q3Xd209gm7nQgTuuWAvCIdzJsyvMfHm8ePH2bVrVxLmZu3mbxZKu/XWW/nd3/1dXvKSl6xpDl01cbqQds7MzPDEE09wzTXX8OSTT6bCMcPSClqHRsiM1KW7r2khO2odzeb7PvV6neLgCCODxe4H6Qg4LQVYFoHjEXqFSLwsioKaZmmaPFMWvXiRS5t/n4bRluOysDyLBiGoWTAFODZCuOQLRfKmKYlTp06h/Rqzc3MEEXVLLp8j5+WSRU9b/dFrjYumz0xbDjqtqVSAjuZu+j67j6p79QI1m1QtjafdyEABwiywYdeDZvSa1ugwRDU5MJnLY2+9In2sPtYvGhFCMDAwwMDAAFu3biUIAhYWFlrSbyMjI4yOjjIwMJCsO+uBWp9tturnir0gHE4W65Zfbibe3LNnT8uOIwvY4OjRo7z5zW/m0Ucf5e677+YDH/gA+/btWzNIoZvDObp8FCUUk8XJFoqam2++GdcbKkVRAAAgAElEQVR1Ux2i1iFBtYS2PAQQhhKflc50Rdbopk/KrVIuMz0zjZCKkaFiumeTKmruJAEixNFDTBWjq1VEhnlpZSN1Wq+Jzpa+UxaWzvLZ9bjBpohIWzauJXELQ+TzeTSCcrVmWK/n5pFak3ddk36Toi8dDpYD1XJ/ByFI5RsDTK0odiS9HIFSmdJyRhupeYzO75i2nHQGAyG7AhPav7P2ldf01bnJYmtJfyml2LBhQ8J5Fqffnn32WZaXlykUCoyOGgTpWhxOvFE8H53OBYdDw3k096a0E292O6ffgn7//ffz1re+NRFKe8Mb3gCcPfnno0tHmShMILTgBz/4Ablcjptuuil5sdMkCsLKatK9bqIKibYcAidvMhjakDbKLLvPPk5paXGRpeVlxjeN8+zJqQxhlIH09uRei4rS2nYQoY8WDhGNAYS+gfE2OQ+RwUFoZadHN5pWRuSeY1mZCEHb0WsCTd61ybvDMDpMEASsVGusLC8yU63huC65XIF8Po+SIkLQBcaJxA3I/aKcDDLVCIWuNvHG0WPREwp0SmRp2+g2EEC7vo5pBM1Anmo70MMpxfOTw6OoTZ3f07Xaegr8sbWn32Li2ampKWq1Gr7vJ+m3fuwV57O9MO+6zdoX9G7Em93O6cWl9qEPfYgPfvCDXHvttdx7771ccUUjzF+Ljk6/c55ZeYaJ3ASPPPIIl112GePjraicfozROgwJym3w06YFPgQDnXXzBJFgmdA9Cvs9TGvNzPQ0odZMTEwglEJlSNoJJdEpOjBC0EjfGbyt+btUaCdmKTZwal33SZtxpkjJyuCUso6VwcEppRjM5xCeg9ZGoqFcLjFzyojOeV4Evc4XkaEPwiPwchDXL+JUUyzJnIkxWoFOuccsaTlAdwFodGQRMjAKCGURlrs7yoSbDbCv6i0ZvRY7W304QgiKxSLFYhHLsvB9n2KxmPT/SCmT9Nvg4GBH8+n5GN3AC8ThZNHE8X0fy7I4ePAg1Wq1azd+2pizs7P8yq/8Cl/96ld585vfzN/+7d92IE3WI4fQ7hC11jyz9AwX5y7muj3dnWK/SKo5umm+n7bsR5LOMhtTBbZK6j0ijOhUukQ3ge8zdeoUhXyeoeHhhAgz9TskheFDa55DN4uL6L0GTGoFGqkscHJoL2927CEmEgpMJGQW/3Qphn71qeSyym5pGO0+1FrGqsSn4LoOrus08b5VWFldpTIzja2M6JzShp8tiSJiEIMyzAPJO6sxm4sgYi8IAjQiG/t0FoZw2+0RkTRqOFpKwqz8bD1ehNiBqU2TyOH+zc9Z7Vw1fjbDq8FsIObm5jh+/DgHDx4kn88zOjqaSGf0amN4vttPnqXuOWBSSkqlEo888gj5fJ5du3atOeR99NFHeclLXsLXv/51PvrRj/IP//APXWGN602pxU4qDEMe2fcI5aDMzZff3DcC63YdHYYElc5dZTtKTSjVNSWnMRFQIC0CJ0dguYR2Dq2MPn21UuHEyROMjIwwPDISOZs09Fp0zabXsWdKTYhMi17LQhXRuAitQWhTC3JctFtAWxbazaNtz1DtdDNlZajxiEzwbGTTWD1TYBL6OEHD+5Znw8WbmJyYSBYx3/c5fvwEs7OzlEol8/krhajXEGGAiJpYRegjwwApQqQUSNtCODYyn0cWCshiEVkcIPRyhionX0B4OfDykTPvs3MQsicVTktKTVodRKsdlkKro7VGKIV9Ze+m6bXaj4tpwHEcNm3axM6dO9mzZw/btm0jDEP+7M/+jFtvvZWZmRk+97nPsbi4eEbX/sxnPsM111yDlJJHH330jMY6G3bB4WB2G/v372f79u1ceumlawpnY6G022+/HSEEDzzwAO94xzt6jrEeZoPYecRUOjPBDABbh3pzqPVyOEFlpSO6ARKBMXNTpC8GmFYJHUVBobRYrPicmF9mbMtl5AaGmvFkTWf1gl5L08VO/0NFRyG6i2WOIkQDwSal4Q3z8miviPYKaCdnmjwzNWaq9GcmZCaFVK1UKrJOCxVFUwLbthkcHMS2bSYmJsjn85Ho3EmOHz/B4uICtVqVns9e2YgoXdpwTHVsIqocHSCFRokQZSuU66ByHiqfRxUKqEIRGf/K5ZG5HDJfQORyCNdD2A4oZUgOhGE1CNOAAoBO+Z5oramPbTZEpmfJzoXDSasLCSEoFAps2bKFv/7rv+bee+9lbGyM7373u7z2ta/lbW9727qvfe211/Jv//ZvvOIVr1j3GGfTXtAptZh4c3V1lR07dqyZ5blSqfD2t7+dT33qU9xxxx184hOfSFXpW2+Es7S0xKOPPspVV13F1PIUAJcMXNL3nPbr6DAk7BLdQGuEI5TqqrfSOliMIjPpmdm5Wfx6ncnJSXNtABX1lugwSsH12xmLtn92iXCESJil+05NyFiPNOnP6Ha9rk5JA03n4riGKSHSVqnbHtr2EsJSk1+UjcJ9v3lJla35NIusQA9UoBANVVMsi6Bcolwus7CwSL1ew3Hc5P/jRVBncM4xEi65TkwmGv87uj/8erIhSHpopAAsLM/BynsIx8OyrabPXCS4fHOqNjxu9boBDOgw+bmBQ2vj3F2BP95707Ue+0k4nG7Hb9myhQ9+8IOAQb+t13bs2LHuc8+FvSAcTjeLCS1HRkYYHx9f80v21FNP8e53v5sf/ehHvP/97+cP/uAPMo2xnhrO/Pw8MzMz7Nmzh3w+z7GTx1BCMV7oTd/RzeGY6KbHLrd5Yc7gEIVUWFLiBz7Tp6fJ5Tw2bNrU2ryoaXTiS4vQyeHbeZQAwogsM+bX6rn4N09RASkLe0o/UDJ0rPPTdyxh6j3xSqjBUtLQ30gbbduABC0Q2jdsA6FhZ+6IwiINntR5RbSlfY9RFqSyM5tFuVl0DjTVqgEfnD69hNbgFIoULNUQnev6HDI6wRRkJFqD1ahNdb0U5hnIULemTptpDKQAFNWLL0OKbMJqWe25QN7ZzjKQldHg+WAvSIczNzfHgQMHEkLLw4cPr8kJ3Hfffbzzne8EjGjaq1/96sznrgWlFgQBBw4coFQqJakSgGPLx5goTGD1qjnQBWgQBj2jG2ik1ITMFt1ASKhDpk5OJTTvXSbRsmiYKCokFNKADaSJHITWSSon2TW3Rzht6ahei6Nu69dvSRU2Ts7klBCyL+pMaNPfIsJ6Y07KMr+EiCIt06BIqBEi7FsL0lG9pZ+ZR58Bnm11IwQVTaJzIwRhSGm11BCdswz4IJfPt9YwlZWaVsxCmRNqnWkzg9UbBp3cSa5AMHoxYuHMahztdi46/Nca4axVC+dVr3oVU1NTHT//4Ac/yJ133pl5nB+HvaAcTky8OT09zU033ZTwWa2lrnLy5Ene+ta3ct111/F7v/d73H777Wuag1KKWgbtkHK5zA9/+EMmJiYYGxtjYWEh+b9jK8fYMrCl7/ntfTj1Srl/6SOOcDLAnoVUrCwtUq/VmZgYx/N6IGo6rie6zME4IS2kWWgiehuhQ3ytmo7KUFeTa4hu0sDSMlu9pS9SLnaeUiF0HRzTM6Sj3a5vlwgdzziHoJ7JkWDZ6cwDGR2qdFyKWlPM50Br6vU65XKZmZkZwiDA931WyxVytt9XViC2tNkHUpk+KdWH660P6KBl7luvMpHQc0BK4GyPuVam6K997WvrmdZPxF4QDkcI0UK8uXv37pYXYC0OZ3x8nC9+8YvcfPPN7Nu374wQZ72smaJmeHiY2dnZ5Dpaa44tH+NFG1+Uep3knDCk6gdg5Yg4j5ExNLhpIQlCnUqHY6jbT1OvVvE8D8vqkdJoi24gvlTKshTR22gEwnEJ7DxCCFPQ1hHaLUt00nTRlitmdEpAqoszNZkMTqkNNBFHTYZ0WZjeI6dgxnKcRq1LhxCEhn07fmcysAVoZSNSKWxEq+MSAttxsB2HwaEhdBhy/PhxSuUKCzPLKCmT6MeO2KGT61l2BpE20ah59TNlQ63/MxUDQ4iNmwinp89JveUn7XDOV+JOeIE4nEqlwiOPPJIQb7ZbLKaW1W655Rbg7PTUNFscgc3MzCQUNfH84nPmq/Os+qupEU5z42etVk3SSuYnyuw2pYtAo3QAQT11FxsGASenTpHzHDaNjzM1NdUdumzupsc9Nk9SNaQMepoh29EYZBaWQivHNMfFi3fgm3TWWhxRP8vqlLJwtEmVCS4twqAB326Zi6kXYdkRNX8QPRJTPBdh0JCaBhPdZKkVSauv8xJSopXFRUMDMDSA7/uUy2Xm5+fx63Uc1yUfsV53iM51M8tpfE4956QyaevIrVcl7/dP2jlksbWm1M6m2udnP/tZ3vOe9zA9Pc3P/MzPsGvXLr7yla+clbHXYy8Ih+O6bksKrd3ORPVzref1quH4vs/evXvJ5XLcfPPNLS99s5OKWaK3FNNTamEYGuhojxReHEmEwkLYNnXlElqeqaeErYtkvVZj6tQpRkZGGIi+DD0Dli7RDcR1lwwQ6ZZzZNc0X9xlrqUV9c8IhGVqJCKSVRZxrJBAn7P1A2UxI3eQ7ixTU3eQjQ4nln6I3x0do8AibRrLQrs5yBejaEhHoK7YKcW/tHkOWdgCmj4ey7IS4kqtNdVajXKpxOzyKsqvJci3rgVuIdC1avRx99nUZGA6EMMbkCMXAeemI/+54nCKxR4Et2u0N77xjbzxjW88K2OdDXtBOBwpZU9nA2fmcM5GSi3mbbusC0VN+znHlo0GT5YaThAE1KrVTGkyg+5V+AizgEvLbK7DkNLyIvMzp7l40ziu3Xhlukka6D7szC1sBpmim2xmdHgikk8kWkmTmhHgC4u6VTLyzBEzdl/LGJFkodbOxNGG6K8KGo8l0wEFCMz1mht4IYqSLCAGMyiE4zSOiJiX0UYwjSAEIVA9Ph8hBJ7r4noew0BQqxnRuaUlZmo1HNtO0m9KKaNCGkkU9Cx5KStTdKMu3d44R+vnRYSz1jFLpVLXTMz5YC8Ih5Nm63U4ZyOlNjU1xdNPP53K2xafc2zFQKInChOp16nX69QzUNsbgEGn4wxDmF1YpFwuc/ElVyAtRaCj+k8YRKtH68orVBq7tG77s7cFoe4a3ayurLC8skwu4hOzksWz81ICYfi4bAcRBmbxExjUmA4jmpum+WZNk6XWbnQ2XrUsbNyCTLWiUIsMTbGyqxMUIvpNWmBFTjxnmAYS7Yq4VyYSR0MD9RrKcShaNsVCIfpRjVIkOheEGtexyXten/RrdJNpU994MWJguHG/EWXM2bRz4XCgN6qym5XL5fOW2uYF43D6CYz9uFNqQRAQhiGHDh1idXWV3bt3Y9u9+wlaHM7yMcYL430h0fE5pmEuQ3TTTaMkDDl9+jSWZTE+Po6SilCHhMLwcwkFNeXhSwdbyijC0An9fjdrCK5li27ap6W1Zn5ujmqtyvDQMJVKhdMzsxAGeJ5LLpfH87yuX+7GvHSyeGohQTpoq3G8CAN0aOpBXZmytc5EYJolutGaSCE1Jd0irXR5bCFMLS5tXiId72f6fCqNGln7peJxtDbIhwh1pjGfsVso4o7CiIZAC0orS6yulqhKi5PzS+TzOfL5PLZlIbQ2jqhWb7A1dHvuQqC2bm/50fMlpbZWW11dPWspteeavWAcTj/7cafUfN/ne9/7HqOjo9xwww2pX5r2CCetfgPmi5/lq9gtuqnX65w6dYqhwSEGBgdIyB6bTANCWdSFQikPoUCikWGA0PTe3evkt5T5S9PfF5lxgKewLZtNm8YJggDHdRkcHkYHPpVKhVK5xNz8HJZlkY9qCkLEkVKWqEuYXb6yQdkRa3YsfWCioQCZie0gS3QTCJnuvITIRq0j09VKs0kn6ASY0PcNkhb4rXWgpF6WwMElyq8z4LkMeC5BpcTYRaOUy2UW52fxfd+k5vJFcpZEtW+6hEwYHhgeQ+RbF+FzkVKDtUUj58LK5fJZAw081+yCw+HHm1KLNTJ27drFRRddlPk6MQDg2PIxrt94feo5GYSEO6MbYfLHs7OzjF00huuZArBQIkqjtF+jkQYxKDKJLwChEFIghelFEUGA0H5EV5ONfLPZ/HqdqVOnGBocZGBwMIna4tqNEJJcLk8u4tQy/SQlZmZnCfyAIAgol8s9ox8gqt10YztocK0hbELbJfTixcA4ogQpF88ri3qoAKl9IKVTXqp0BydlNqeUSfnURtSqhAkqocsxgobMdr+xujBDWLbNgG0nn2O55lNZnGexUkloefIRYzKEcdgE45d2jP9ciEbOhZVKpQuw6PPZ1hOpxOetxeEcO3aMY8eOUSwWMzsbaDicBBKdEuHoCF6blk5riW40BH7A/Pw8E+MTKKspzdNrGEFyDSmEKTwnp2gCDRBR5AuHmvTwpcJV1v/P3pvEWHJdZ/6/eyPivRfxppynGjiKkkWJ4iDJggEDXkgNGL0w0Bs10AvDq4bb3nhhwIDRi7ZhGMZ/Z3jhle3ubbcXHhZe2LB71Y2WbbFIqkgWi+JYWfnGzJdvjuHe/+JGxJunrKRFsuoABRaz4sWU8e6J75zvfN9Sttg4M824hdbZ39sjN1XXXvQe6jgOjlOmVCrjByGN2hm9Xo9mM0E/nun9jBEg1pqAt6y4ejR2Q6Q0g5y2Mzk/Iy0SDbl5CUNLOzZ0W6Evt0Yi0YjVYp9yHQttPTrXZQjHcmbQzUwIuZIJJ4TAzeVwrR22IX0xaLVa+L5vZPo9j9yNZ3Cysz2NL3PCeYJwvuCxqocTrmO/OxVJeWxVJBI1Sim+853v8C//8i8bH0drzWn3FIAbhRtLtw9jIclVCScJrTS1Wg2N5ujwaCLZCDGfUGD+bSQ/s7whjCnLSUkkbHyZBStrdB0ThWIVzLyBR1FEvdHg+OgIe7rcIuVaSULKkRUwxOin16feqKOUIpfLkXU98tnMYgoVxGW1VfdTx3I4Oi4FWWa2xCbdtxgrz2m5onSzJrrZfPh0wRYxujFbz0c4GmANl04tV+veTcvhWJaVmpahNb7v0xsMuNvsEvzzP6eGZeVyOf1O/KzLX6viKn2mJwnnSx7LktGyWEemZlyi5tYtg0yugqYAPu18CixPOFprur5GyYzpXSyIRNcsDEIqlQrFUpEwmjcJvmQfcUlNINYT/BxntWkzhKqI50ikE/dsFDKKaFTPUEpxcnIy/y12nV+XlMhwckPHcXDKDqVyCa00g4ExMms16tixlpg3rSUGBqWtmuHRzGXVTeu5adtBRMTGcHm0m2OMAmZoyVG0ViJZS+xzLXTDZHJbhHBsG1YNScvV6AZY/swIQSabJXPjabaf+jnCMOT8/Jxqtcp7771HLpcjCALK5fLq4/wM4yoo7DrncD5v8SThcPUm4aqSWqPR4J133uHrX//6xtYH8+JB5wHAUkq0HyqCUBPiMCSHTw5LKASRQRJjlzroD6jVa+zv7ZNzc3S73UkTthWJOEE4SV99aUhhym5LtjP+OnBaqZHNeihXEWULRqxemfKU0MqUa7TPKp2UVWUmIQVuvoDnmhmtIAjo9XrU63UiFZHL5vA8j2w2u55x1BozPEbsc5S4TA6OacbmJ8YgzslAOJLwj8UF4qZ8bPeg1HqJZG10M5Ukpm6vFmI9G4Y1VL3XEftECDh6GjCDp/v7++zv75veT7/P3bt3+eSTT/jwww/Z2tpiZ2eH7e3taxfffJTYdOgTnkjbfCnis4Dei3o/iyRqHjVOu6fs5nZx7cUc/f7QJMAkWSgNSkvANL1tYaRsLi6adNuXHB8fp2/zswlmds5mIuJ5Fr0OukHMURqYjDAMqZw9ZKtcplAsmgQIhhkmJUg7trhWKGRsGBbOTyxSGur1SurW6Nwdx6FcLlMul1FKGeZbr0e10SRnG2LCwgSsAdbo5wkL1CqLhTH30HFvmeQvQqJlxvSPotD8UECYyaHdfJy5I0NV16y2vYYZoVI9o7uNKfGtKiEvQjfT920dlL97jJjTuxFC4HmmD/f000/jui4XFxc0m00++OCD1M55d3eXfD6/9nf/80KzjqJo6ZjEFzkem4TzWcQ8lloiUZPL5WYkah41HnQecCO/uJwWhIogNF9kMQ92aAgUnNbqgODwxrMGLKAMi2yMdZaU3JbFQhvoedspFSOh+dsbj5YqR4eHS1UhdKw4HWgQwkJYtmHEJfMx2tgcjM/QLPYAWmw/IKXE8zw812VXCAJ/SK/XNzbOp6cx+nFHzLc19Nc0Yr1hUCFHStOLIlazTvGPBssydggGjsVkDQTY5r9aJCXQhFCiR7AyGKaznRDfs7G1VwuxJjNt/vOuYYTWLGfCzG1uCAFHTy0/VtzDkVKys7OTWm0Ph0OazSYffvgh3W6XYrHI7u4uOzs7Sxfyz4OszZc9niScR4jpkloiUfP0009zcrJcCeAqcdo9XUqJTtANzC+HhVHEw4enlApFyltlQGDykwRshjpDiI2NNbcXMS/W6n2lyW/+NPnlZYtWq8XNGzdWTo4LoYkilV6fRkOEcYgUEiEtsDLGYweNFiEBVryIT13TOucuzZCqQT8OnW6H46PjFP00m00s28Zzc+Rz7vLzX8vyQKwnrcMa4E2Mm75NDuWmn5UGMyLGpG6EQAcBKjdEe4UR4zGhfqfEBzVJcZfWYuuEcVHSdWjxC9DNeCxKENlsluPjY46Pj9Fa0263aTQafPrpp2it0+RUKpUmPv9ZydpsknCu0kv+IsWThBPHVdRnxwcy15GoeZSIdMRZ74xfzv/y/H+PNMNwtKCa1sDo4R0Mh9SqVfb3dtN5lekQ0iZQFhYZtNZGPl8oMy+iNNMyAtPN8PkxokubF+xJ5NFo1Ikixa1bt1YvoFqjogiBGNkja6OarNEorQwTQQgkhimmhUQ7OQLbjctxJhGhIiwVGsXlVey0qZBSxNPyZkH0w4hB55J6o04UReRyObwp1QPNesOgRhR0ldSNWE+EdB1FBGkjwvEkYRKK0ApLJJ4+Iu6dxcdGTHnaiPRei9jzhwktHI0KI6JM1giMptbRceLScfJKfg8L5m6mY53vqxCCUqlEqVTimWeeIQgCzs/PefjwIffu3cN13bT8Bnwu7A6+COy7q8Zjk3BW/QITtLLJw5HQqd999106nc5KiZrx2PShuoguUFpxUpiPnHr+pK3xOMK5bLe5bLU4Pjpaen7JZwwgEYYshQVYCKHNAoRC6Agp1EwCmRdSClTKlhshHKUiKpUKuZzL3v7WQkmcdMgzvl8i7leMn7OwxNi2Ah2F6SySiqVSUnXpOO1ISxIIC2Fn42PrVMol7QsJuVqCR0PGssiWypRLZZQe9X4S1QPXdcnli2SmLnLmbVas60Q6y0ybqZ6K9SytlylCJD0cvWgodmJjsbRXJFBkHBtpSUTSU5zcQ/x7FejyPmQWl1WTuErPxXEcDg4OODg4QGudDjq/8847DIdDlFI0Gg22traupRS26UvsE4TzmESScDZp1kVRxMXFBeVymVdffXXthz8hG2zyQJ+rc4C5PRylNEN/8m1WCIHSmnq9ThhFnJyc4NjW2OI/G+NEg+nQWhBqQVJ+swQEom+0xxZJtIx58sT/i0YTBD6V2Oogny/E7LU5dOKxpKnR8XzLwtM39Xwh0LE2WRRFNJpNXNdFx2rSmhEyTdSrR215kVK0U9M3MoYhp6P5MzFTvRspJJ7r4Y2pHvR6PRqVM7Qy6MeNfWRm7vHavZvr8uqZRjdj/zY2h7PenM+qRVUbKZ8F+zJo2bD42F2vHP2o0jZCCPL5PPl8ntu3b3N5ecn7779Ps9nkpz/9KY7jpOjH87wroY5NeziDweBLK9wJTxJOGpuqBrRaLd566y2y2SzPP//8RsdKyAabPIiNqAHAzcLNmX/r+9HMm1GkFIHvUygU2N3biwllKxYhgSmbrVyrTFLS2IRIhmSNAr7QyBgBoVWcSCZ3Nhz6nJ9fcHh4QCaTNaBnCWMpVTKQElZ4y4ix8l0YhlSqVcqlEoVCIe73mGONox8hRPpn9ioN7kEalIcFge0SZjyzQEaRSUrSaMjNC8dxKO3sUC4VUzpvgn6Slw7LsrAdZwMn0nm/oFGP5JHRjdmduZ/SRkSrWG6rCQXGtmLlKUFxZy10A59Nz8XzPL7yla8AZvFPkk+v16NUKrG7u8v29vbaL6ZXsSZ4knC+BLFuSW2d+PTTT/nkk094+eWXuXPnzsbnssz1c1E0wga2sNl3JyVxtNYM/MnzHg59qtUKlmWxvWXk3K2J0tb8MAv26lVBSoOexmnOilgef7wEh0ZaOkUHg8EA3w+4ceMEyzKPnuFVzR5Ta43jOFQqFVzXJe+5q7/kMQtrOBxSq9XY29tLkUQqZmrbCK3QWqT6dMmfZLvx/84cQsqkC4SwHbSKwLLTVGje1GMjuNiJU0YjqrrneemMRbVaRWtNvVHHDyIKuWyKfuYef93ezTpzN3J5UorpGGuYzLGWsZ0SEnsFetMC9JroJonr7HVMl9RzuRwnJyecnJyglOLy8pJms8nHH3+MEGKCfLDoPDZ9sex2u19alQF4jBLOqlgn4SiluHv3Lkopvvvd7165xnsVsdB6WOfQO8SasvMd+GoikbQ7HS4uLjg8OqJSqQDxm/patWG9shKj0Wg9au4u2q+QkkgZPTWtJbX6BX5gUd4qI50cWkdGmn6uD49JBPv7+4RhSLfXpRELcebcuCHvTi/KRu2g2+2m1+/MYYwlOVKIKeLBVOKJwmAp+gFiaf3kvoz9V0jzR4JwcmgVMOpfKcOgUxFII+WSyWZRUcSg1xv1fiwbz3Nx3THVgzm9m/T3EjdB1kU3KwkF2iCl5Srb5pzWokuPc64XRWEbcj+7xXYZGpFSsrW1xdbWFs8++yy+73N+fs6DBw945513yOfzKfV6fO5uU8+eL/PQJzxJOGmsSgKJRM3x8TG3b99+pDerKyGcoMFxYdINVGtNZ6jN7IM2zc4gCLgxJQdjydXIRaPN2/uKjGPF6AZIe8iy2MUAACAASURBVCBzdpYeL4oizs7OyOfzZLNZFOBrB3CwpCEhpGU4pdCxh09yf23bZqtUhlIiRWNKUo1mA8d2zKLseTiOw/l5k+FgyPHx8fyFQ8yX4JmXVFRMPEh6P8l26QULYdDNstBmAFPHpIT4g2amxZKojCnPWZksKEUu65HbMgyxYDig32lTr9dRKiKbc/FyWdxcdsGzN9/XaO5pLendjE5dr+4nAQgL9BrDoEFvsRhocswN0c11xyblr0wmw+HhIYeHh0ZOqmteiu7evUsYhqnuWxiGGw1+f5mVouFJwkljWcK5bomaqyScWlDjRffFiZ/1A+j5FkoJqpUKXs7h8GjfUIIn3oRXoxtLilioc32WzCJatJQG+QyHQ6rVKjs7u+TzHpeXl2my0lqjEGhixpK20TELTkqNhRnitMRIyUBIget5uJ4HOm7I93tUqzX84YBM3ORdiEhWCCckVyV0hBUvPOPIx/d9NKDi0stKpuE6Df5kroW4CxPTiy23QMEtUBAmefd6XdqdNpVWnYxlkXdd8m4WS458g5QW14NugEhaWGtQ3tceBtXLy186XwL3+scJNomr9oSEEKno6FNPPUUUGdX1er1OtVolm80yHA7Z3d2NPZoW34cnJbUvSVylh6O15sMPP6RWq/Haa68tnYDfJDYtqXWCDp2ow5E76XPeHoDv+1SqFba3tikUCgxCs7DaUuOHMU14jb4MiKQFsngLOUU8WKg0oFPfn8PDw9jbxBwjWezGkZIZeFdxGUegtSTCQmOP+kCYN27TnDcMKifjULAKtNsdtre3cGyHTvym6WQyeLEQp2VZC9HNzDVOJaUE/QwGg9gnaB9hWUZSZqykJuKFavw5W8sZVMjljLJ4oS54HsV47idhvtUuu2bux3XJZrMEdgadK8Q9JB3PtxjkmJzLqt5Nesy5Qq5Tm1mr6NKYwdJgOMF6m7uv3eUK6P8WcV0kBMuy2NvbY29vDyEExWKRMAy5f/8+g8GAcrmc6r5Nl9ueIJzHJKaTQBiGKQvtuiVqNkU4px1jS3CYO0x/5oeaxnmX5nmTw4PxRd2sNUEkCMniqwwasEU8O4Oa+d6LmFCwUqyTyYQ0PVwKhhzbPL+g3+txcnIy0ecaT2jpp/RIPXv6pcASpmMRJT0jLNMXASwUvj+g+vCM/d0d8rEAZz6fR2MScb/Xo1KpoAE3l6PguWSyi0pS8QXN+b20220u222Ojo+xLSv+vDXZ+4k/p0mSlFyJJLTWC3syE6clBSIabTdP863T6aLCgLPq2cjvx7YhJmfoeMYFrcHJmjM1tL00OYlYOUBLYUzzVomjrqNmLSyEDuNrnb8/7RYgv7nq83XPrHxWSgOu61Iul7l58yZKKVqtFs1mk48++iiV5dnd3aVQKHyplaLhScJJY9zbZhOJmqsoFGxq+Paga1SiD7Mm4WituffBQ9oDbczSFpEXlCIRH0gGOMGgH1sqpDBsKkm8UCIWUqeFmKVViylIpJXmYfUMy7I5Pj6es7CbBU/G+9IqGchkwWK0oEEOXPYMZfXw5Cksx8HHWFwng6mZjCSbybC1tUWkFINel9blZWrslYg/TiREk3EmjnNxfs7Q901fSIj4RoxYZ6mSQEK7TpNQvIAzSqTT90NrVipaA0ulYBLNt0wuhwp9draNhXO9UUdFamLuR0g5oVQdn1QM6yR67DFSboiSFtotjr1pJOU/bZQnosAgJ5WgqalnWsiRd86SktrPuneTxKYN/nVimqUmpWR7ezstzfu+nzLffv3Xf51CocDNmzepVqscHBxc+bi//du/zd/8zd+QyWR47rnn+PM//3O2YsbqzzK+fHZ5VwzbtokiM/3+xhtv8M1vfnMtPbSruIVuak2d2BLsZwxr68ev38GPbI6Pjpcy5YSY7/oZKsEgtOgFDoMowzCyUFjxJMfihDPvh0lRKQojHjz4FNf12N/fn7u4JPlJx6SCZclmWXmv1WpxcXHB0dFRiuwUECIIsPBFhqGVw7c9AtsFJ4dX2mb/8JAbN25QLpUIAp+zszNOT0+5uDjHHw4nSABaa2rVKkopDg8PTbJZdB8YDZ1aUmLbDrYwv+cEBep47mecCbdOmAHU1b0UYz0hzNxPqcTR4RHHx8fkcjl6vR6nD085fXhKu91ebhqYCJpqjTSvIPEArOm4iRgpCSkQlg12BjJZyLrg5s0frwBewShXewV0vohy8yg3j45/rt08Oueh82XDTtswPgv5l88K4SzbZyaT4ejoiBdffJF//Md/5Bd+4Rfo9Xr88Ic/5Hvf+x5/8zd/c6Xj/uAHP+Ctt97ijTfe4IUXXuAP//APr3oJ1xqPDcJZ9XAKIajValxcXGwkUZOU4jZ5M9q0pPag+wDP8rACix/96Ecc3nwey91b+hkhQEh75RdTSggiSQAMVZYw9CloZ6z8ZpLCPOST9DsScsAynTazvUEHycK7GNkkyXLyZ0Z7rYFSiuPjYywpTe9nQSgNaIEWNqHQIBzDVnbyFPNblFFEgU+/26bRPEeFPtlcllw2R7vdplAoUCqVRscXpKhlWYj45iQq0hOU6xQJgUCtSD4jQsHyA4q5243P/WggGg7p93vz0c/MM7KE9WZZy10/k99tnLjA9LMsKdLnKTlvtXO4OIsvic+LlcCq2GQOx7IsSqUS/+E//Ad+9Vd/lcvLS3q93pWO++/+3b9L//69732P//W//teV9nPd8dgkHEhovLNfTN/3ef/99xFCbCRRA5ujFdicNHDaOWXP2ePjjz/m5ZdfoatLrNJ3lJKVrDOBnqqCCLQW+NFogNOSpOU3gWIcdwgEfuBTq9Y4OpzsIy2KIAjMYiHFkmQzu35GUUS1Wk3r4etaI0g5Wes3PSEgYcc5Nk7ZZXdLI7Sm027xsFrFlkBsSOfFtGu5jrYaYmabadq1odH2CIIAy5KosRKdIW+I9ORXNuU1EPdIlsr+SInj2DiOEbKcVj2wbZucm6eQdbBtO53rmbuvtURILcTYM570tibCsiF/tTLPo8razItN5abW3eemSgMJaSARHX3U+LM/+zN++MMfPvJ+riMeq4QzLxKJmpOTE3q93sZvTVcZ4pRSEqzhnAgxU+78Q3bY4fbt2zhuibC9zucWJ9gkLGncjJOYt71S4I+JLUphEpBAcdFqEQQBt2/dNjptS46ltSaTcUAITk9PcTIOnpfHm+qjmPOYTDhBEFCtVimXtygUDGV0HmHhqmFJM0/UHwxoXnY5uvU0mWyWMAzpd7ucn7cJ/SGFXIZi3sXLZtIS23RM97XmRbvTodNqcXJ8bNhtOim7mYSeLPZy5aQkMfV61XAmM4lrWvUgCAI6vX7sdqqwpIVtWzMIWUsLsQzdJPufTpRaz1yNLu6aPs8V4mdR/rpKbKo00Ov11qZFf//73+fs7Gzm53/wB3/Ar/zKr6R/t22b//Sf/tPa5/BZxmOdcBKJmldeeYUoivjggw823sdVZmosy2IwWO35HkURb775JtVhlW+fGKZcew2r+CSRrEqe0+v1vIRjWZNJSWkYBIJqtYGUWbQl0DJLOFbnn46khObYNgf7B2h0zCLrp2oIrmcozNlMZuK8+v0BjUad/f39iQG6BVWkiZBizaSkDVHkstXi6OgoLY/atk2xXKZYLiPQ9Hs9Lvs9Kq0WlpTkPZdC3iVj2wgdoVWEFQWLm+Nac3F+Tm84jJNNotiQlBbj8lssUqrDIPUQnat6oDXjJIeFrDIhWaUY4GQybFsWophHKW2GaH2f09PTWPHaw/NcLHt1EpxHvZ4p7QqJLuys3Nei+KySw3Xvc9Ne0yYJ5+///u+X/vt//+//nb/927/lH/7hH669/HjVeCwTjlKKt99+mzAMU4maXq+3MVKBqyOcVUmq3+/z+uuvUzgoEOiAI/eIIBKI9YCRiSULriWny2nzG/XTHw9DoxxQKpVwXde8EWuJH40jIG1KcDoaKQeM7UsgyGayZDNZwyKLInr9Pq2LFoNBL33zDqOITrs9kQTiy1otRLpmSCFoNhsMh0OOFikUaI2QTHjgmFmYPpX6OVEUxXpvOXLZPDKWoDEmcPEMTBRSr9UQUnDj8HBh+SuxW5AItGV+QdNkgzT5SCs1dFtWUhPrPJ9CIjCoREpBJpPBcRyKxRJhGF9rrYEIh+Ry5j5ksws03+b01QxoG0NKhe2Usn2V+KKQBmD1i994bJJwlsXf/d3f8Ud/9Ef87//9vz9Xcz2PVcIRQqQSNYeHhzz11FPpw3CVxHHVz61KOM1mk7fffpuvf/3rPFCGoXbkHTFUGVZ1SeRYmWxZSW0+6Wxye0syYVUwGAyp1ars7e3jujnCMIq11UbbKE3cA5JoLdE6wrEEloiQQs8dhrQsi2KhQLGQBzSDwZBm08j0ZLNZut1u2kdZdV2T17J6DuascoZtWRwdLm5eSzmLEBIH0HK5hFKaQb9Hp92mUa/jOEZyx3M9LNtGqYhqvYGb32Jrq0yoNULECSkezjRkhIRGHdtHjz2byfmOM95QGtRI9WD+jZCgVrylCGBqpiYp6wkxutbS1hYEQ/r9QSzlYno/45pvWsj5jqUTJTWBLi4nvayKL0pJbdO4rsHP3/zN32Q4HPKDH/wAMMSBP/3TP33k/T5qPFYJJ9E6midR8ygJ5yoltXnH0lrz8ccfc3Z2liob/PPH/wzAfu6Ibt+iiGCZhYAUoyLLooVZCj1RJmPF9gDtdodW64Kjo2Mcxx5tH4Vz/HP0mKCoJFQCJUS6nSU0llSjuZn4YqQURJHi8rKF67qcnJwY9BObZIVhSC6XI+/NE++cukb0UjMDFSnOzs4oFDzK5VVDh8uTm5SCfCFP3nNBa/wgoN/rUY1p1WEUUS6VKMXHURBPYgqTECzbcDSE6ZQJrZCWEy/SJrEYrbko7R1pBEQBOk42CdV53HKBeF+rQgsLyfTzONW7EbH1tZBjvR9NEISG+RZrvmVyLoVshuwU801rnaoxaK9kHD8fIb7MCec6Bj/v379/DWdz/fFYJZx2u71QouaqCecqLLV5CCdRotZa8+1vfzt9q33YfQhAwbpJM7TpDo30v2NpbGnelJMQYjUJAExSiuauoaPGiBnONP/bbDbxfZ+TkxtIOb3IzxTh0mSTLDhSTJq6RVoQRWPDcICUCu37VB4+ZHurRKlkdLVs207ZOmaqfky803HM4ud6WPZkY3YZAAqCgGqlys7O1sq3SUP9XoMKncjcCFOOymQyuK5ryA6lEkEY8snHH+PmsnOHTs1JgxICqSFKJBViH56J80EjlUY4WdCaYa9H7aLN4f6eEQZNkBACS48z4Bac+xwmXEI6GW0k5+RdM/fjOGVKpTIKGHTaBv00Y/TjGnFVDaNkWXo0dGPO74tTUtsknqhFf4ni6aefXohGrvrwXiVRTaOiwWDAnTt3ODo6mlGifth9SClTQukdtO4AGOpyKEjasrbU2JZRDxhfE+YlHCFmezfztpcSglBTqVTS4bQZVqsUEyyjeb4ysJStC5g3/uHAp1qts7d3AzuXY6hMH8hCg4iHD4VxaPRi8U4/MMSDaq2KVtoQD1yPnJtdiNQGgwH1ep39vX1yudVv2YkKw7IQzJbv+r1eqiXnZDIGrQgYDgb0+yOyRJJ8EkLESt/MmNKtCdEIur0eFxctjm4/nfa5UoHUKIyfs6SfpBNqAqnOmrSQc7XVRnM4GrGWjI2Q1gj9aE0QBEb1oF4niBUehFsg6+QeeeL8i4BwrsKifCJt8yWKz4KpcVWEk3zm4uKCn/zkJ3zta19jd3d3ZtvT7ikH7hGRshY+wKEShAqktIxUVox+ErrteFgL0c2INCCAwTCgUqlQLm9RLM7/AshUd9L0ceYnG73weEl0u10uzuscHp6kfZpICSIskmVOAJalsHTsKioUGSdLZitDeauMihT9fp/WZYtadUAul0sXc2mZRcQw0S6NQoFjr+4Dwco+kLneyT5Wu31Ju93h6HikBCGlRKuIbDZLNjsiS/T7fVqtFr7vk81mKbhmGHPZwiclEMHl5SXdbtccZ2x7EcvVSCRYI+abimVpUuabbVQMlDVKvEl5M7AHYNsoJ4dWRv4oka+Z+y0SU0rVQuBkMjiZDKVymfNmE4CzvqL2z/9MLpdjd3eX3d3dK4nifhESzlX25/v+Rjb3X7R4rBLOZxGWZeH7a0jCj0VSUkto2a+++upCW9mHvYfsZZ5a2Si3LQgjsxQk6KcfOOBLsjmJJc1b7bIlNjnGcNinWquzv39ALrfYy2M82Uz3DkbXytx+kdkBXLQuGPS6nJzcRMrF8wpmOl/gK/OODiYhSKGxhEZYCq/gUCwW0EoxHA7p9Xu0Wq30vJRWHB0dxSSAJTcivR+s3M5U3OIL1Jrziwt83+f46CjtWST/Nh2WZaWy9gDD4YBB1/TKhJBpMz6TcRjHiToKOW82CcIwRp6zKWD8JwnzzZyGeRFRWsWs6gilx4ZT06FTGywHJS3jkzRW/pvCzMQ7NP0mnVxr0mc04qDKzpBxXZ557iWexrzJN5tN3nnnHYIgYHt7m93dXcrl8lqL9GehNHDdw6SbzuCA+T38rMt6n2U8STiPGFcpqQkhuLy8xLKspc6hWmsedh7ylaPvrcXMmnecKIJBYB5gS4CMBLbUJgGZo4x/gjAIqNVqHB/fwLYXf1mSWZ8oiuh2uwt8PhaX77TW1Ot1hBDcuHES21Mvjuk+UHLmkRaxmnRyjQoEWNkMpVyB0lZErfIQHQ8znj48JZfNks97uLGg5cJY434nOUlrTb1WQ1oWhwcHE4w3IdYwawNjsJbJsL1t1Mr7/R7n5+cEQRAjNhc351Kv17AsycHBwXzJ00RWZt75CmHuD5YpBUYjEVWdJCEStKoNXXqpukLCdY9RniC+9uTM4vvrZAgLuwYJYVS98/k8t27dSv1jqtUq77333lro57NQGrju2BThXLf69ecxHquEs84b0abNyE0HP33f586dOwgh+Na3vrX0WC2/RT/qs5s9WZpwLKnnSt1Mf0ZKSRAJgij59xH5QApFs9kkCIY888xzc8gBk2GouZq9vX16vR7n501sx8FzTQ3ftu0ZJYMkoigyhnH5POVSeR2wseagpzaJS4PCqHhXKg28/BY75XJKyx7023S7HeOb4zjkY1O38VkfKcRaZAGtFSqR3fHmM97WAEpIIUZIiXjotFiiWDQyNMPBgE63Q+XhQzKOIVKEQTC3/CLXOqIAFc5FP1EUMRj0yeWyqDAE5qPX0a7kUkVrwJTxMvOb4eP+MVrrtdDP56HBvyqugnDgsyn9f17isUo4q+IqQpybIJzLy0vefPNNvvKVr3D//v2VD5ZnF/j/vvOX5GQ5ddGcF1JANFdxeYwEIGaTUkI+GKiISqVGNptBkcHYButY/2reMTVh3JhJxSHjJnEvpgNrrfHcLF6+QDaTTV94Az+gWq2wvbNjzNHkal80wayQ59ztxpKSkcOpsLW1TT6fNyMrWiCFheOWcdwyRSAMA/rdDs2zJlqFFLwcec8Mca5zvDAIqVQqbJXL5Bc0e9dBN8uU4YQQOBmHfmPA4cE+2VyOfkIVjyLcuF+Vy+UMgljDGnq+mrcwM0O1KqVSGc8rQOSnJdPx7SYS0BrXN8ChsKRkOr7vddDPZ6EKcN1xFYTzZUc5TxLOWFznTM10nJ6e8uGHH/Lyyy+Tz+fX4sn3hg6HuWcB0on92Zg/UwOTCceSxpRtOoLA56xiHEOLBY9PPu3T8+NGd4yALKmRYjR0KIUCJt94xRgdeGtrC1RIpzfZELdtm263y8HBgRH61GtVrWbkdeZeKzoFJCkTbUoOx1zT5DCrbTsUy9sUy9sopej3B9Qv25zWWmQzNoWCR9HzsC0xIV6qNQTDAdVqlb29vYWlHynEymsULC+5BYFv1Lh3d/HinpqTUMW1ZtDv0+0Zp1NpWZQ8k4CshS9OYq4IaZI8d3a2cT3PJBU9a7U9wUaUMrVGWBZ9HIpXeHNfhH5OT0+Joii1bl639/NvGZsinCAI1hLA/SLHk4QzFpZlEYbhRr/0VSU1rTX37t2j2+3y3e9+dyP0dN6dXNDnybk4liaI5n/REnO4RUkpGdg7ODg0CcGamg3SgmE4KrcINJYIcWyJJZNZjfnnPtEQ19BoNmjHfatGo4HneRQLLkKsutd6ncoWlhBEWtPpdGhNaaKN7sdsH2g8pJTk8x6lgofSiuHQp9fvcf6wARg0l/dcclnHoKJGnRsnN8jYlim/zbSw4j7IipBLyoXDwYBavc7BwQE5Z3bxkmLKgsAf0ut2qdZqqduk53pkcyOnU8HsAQPfp1qtsbe3Z7ZFTPRups3mkv8qDagRGWWe1TZZj1APHjkhjKOfZP+5XC5FP67rpu6Z12UH/yixKcJJFDW+zPFYJZxVb2HXjXCCIODOnTtsbW3xyiuvbFSb7fvQ9ye4RnO300ua7QnCsS1NOJWUWq0WnU47toG2Ab2wcZ/KqWiNZUv6QaKbZhCQjBGQiJvGE1ToONlEUcStW7cRUhAGoSm9VaooTSwM6ZGdY/88La+z4ARRQnNx0WIwGBh3zjlf9GULe3rPSOZYREph3t7aThUPzi8uGAwGKBWyt3dIJF0G8ZCmFDpWTzB/pAhRiVrAksSziHrd63U5P79IadyrSlfGgM2mvFU2VHGlGPT7dDpt6o06GcfBdU3StMZ6dMPBgHq9wcHBAU7GGd2scP45p4lLWsgoAGvMbnvKahshEG4JrRvX2ptQSpHJZDbu/SyKz6KUdRWl6CcJ5zGK6/S2abfbvPnmmzz33HMcHh5ufC7nvdVfTik1oVqdcCYotVpTr9dQSnNyciNdBByLufsaL6EIAWpsm3EEBCbROBbYVmT6Kco007PZLLs7u+lp2I7NVrlEuTzyZWl32tTr9dT+2fO8td8OpdRUq4bxdnh4uGBh0+uADeSCnpJlWRSLBYIwIKMiyuU9BoMBpw8fYkmJ63nkPQ97rIlvCct0ZoRZv8VYMhKxrI9U0VxyQvvykk63w/HxEdKyVje6GM3QjK5F4uXzePm8GZT1fTq9HtWzh2itcV1zjzudDkdHh2kJTmjWE/xMDxz3dCDt/aXPjbSJuJqKx7KYRg+rej+r0M/nYa7nuoQ7P8/xJOGMxXUJcVYqFd5//31eeumlK00NhxFcrpFwLMFSvTCzCETpfI6x0D7D87zY33wsEc35fKJSnJRTHGt5gtMIgkgTKgs/CKlWamxvlyiWC6hk2j0Z8xizUBj3ZUnmZ87OzkAr8gWjLJBxnLn1OxUpHlZOyecLlMslFiFBawnpYuIaFmyTJGopLW4cH6MgPecwCOj1+9QbDaIwjJWjXXJjZSyD0sbpwvF9sDAqBBiUiNY0G3WCoc/RyS2kIO63rIJm8/syo3+HTDbDbjYD5SIqUjSbDS7bPSxp0Ww240FZD8t2IFo1W7bgeHHiSZN+cZuLdpt+v49t26kPlJTykWZOVs3hzOv9NBqNhejn8+KF8wThfIlinZLaoyAcrTX379+n1WqtZVO9iILdaAtaXTMvk3FMWWl6HRVCE6586RUkKcn3fSrVCjvbOzNvUZbURGOJZBLVjB14nQa/hG5vSK1eY39/n1w2x3BMFcVQsZVpeUg981Y+XsZCGVOw8VmUvJdPhTvDIOTs7JSdndlrukosYswpFVGpVPHyHlul0sxtsB2HkuMYJ82YeNDptGk0DGJzPW+u0dw49Vpj1CLq9QZCWOwe3yYUgkBrrFgJwDwGpi9kpH4SxWmDksQkmJ0TcZLQhjEZRRG3bxkppeFwSK/Xo9Uy6KcY+xM5mcz8XS4puaVHkxbV9oCPPv6Y1157LXYSNUrXyXcmiqI08WzK6Fp3+3H0c/v27bno5zqcNafjSQ9nNh6rhLMqrjrECWZQ74033iCfz/Paa6+tTG7JW9W8N6DaZbxPJQiHyXE0g34Ys8TAXsA6mziGMBIxvZjBdHh4SCYzqxxgjY1RGLuB2WRjCU24YjgTjKzLeavD0dERjj2bcLUWKC3pp+eu00FUS4zESAUaYdkUi0WKxSJaawb9Ab1+j2azgZCSMAg42N/B9ZYnm2mb6YUxZ5swjGnPW1vk83lTcluyLxETDwp5U7bxfX+CKu66Lp6XJ5vNTEjiKKWoVqvkcrnUQhtivbp4o9i8wPxJNOxMHQspNVh6DEPFf9eJlppCKIUWmmajho4iDsbKj9lclmwuy47YRfmDuF91TuAHZHNZPNeblNxZo8RX6w75tNng1VdfnSBwWJaF4zhp4kn+m3z31kE/j4JI5qGfs7Mzut0uP/rRjzZWPVgUURRtJFPT7/eflNQep7iqYnQURfy///f/eOaZZzg+Pt7oWNMJpzOA7nBeL0UQKJtOP2bnOGaRGX189jOWBYOhz9APODm5MTe5CUZIKRn8u7y8TIc3032tmpfRmouLBkM/5PhogZHZ3BCpFlz6E6HJWPGbr4jN3BC4novruXQ6HS7Oz8kX8ly0Ljm/aI0RDzIz90KyvPQIs3RpMMlikva8eFZmYl9y1JYZp4orpej1+lxethgM+rFytEk+tVqNYqlEcaoEu2w+Z3S8caSUANH4Hggr2RGCiFrjHDtbZHt7m0Ak6Sv+hAahI4Rrk8/myW9rtIoY9Pv0ux3OLy6wpCTneRRy2aWL6UWrxVkfXn755YVlpXFUk5RvkwQEy9HPdZXAEvRzeHjIcDjkq1/96ka9n2VxlR7OE4TzGMVVEk6tVqPf7/O9731vI1i+iE6doJuFoTW2ZWyekxBoso7GtpO3edOvaDSaE2WTeWFbmlDJFNUcHByYN/JaFTSmH5H3kNnF9GWtFNVajayDadovqetMl+/mX6IgUjKWrAGwDCVbaloXDYb9HicnN8jYEhWXaHq9Hq3LFv7QzPyMLADEapYbs0oGiXrC4eFhurCOxEqXnvzC0qOUkkIhT6FgkJJhkHWo1armjT+KBFB3nQAAIABJREFU8GNVZYgVCtZiT63Tm1JUzs7wPHdCDSEu0JEcUGoBWCPZaungFHM4xW1KGMTX67Q5a3cJgsuY9WZKhslwcr1WZRDAN156eQPiRyxNFCenBPUkSSj5u2VZKRnmullvUsqNez/LYtMeTrfbfYJwvkyxTg9nOByutS+tNR988AH1eh3P8zauAc9LOJEy/ZtFIYR5F5VTr+wawSCAVFpZB9Qrn1As5o0W1pLr1rEETPIFnn0j73F50aAWROSyObx8fkKDLApDKtUKxXyB0lbJCHktu+45SGI6bKnHko0JpaFaMfMwewe3GYSCUBkSgmVpvIJNoVBCoxgOTOnt4uICSyjyhVLsGLrgcReMGcbBZfuSTrvD0dHxxIIhWL20W9akRM3CiBPJYDCIqelWSutNjOYKnou7wmjOCIwuP14YRlTPTtkql5aSWFaoGQFmUHarXGIrZhgOBqb81ry4wLYsIqXIOA63X/jaIyGQVejH9/20H3QdSGfeftbp/Vwn8+0JwnnMYl2EE0URb775JplMhm9/+9v83//7f6/lWM22WPr2n9gmh+Hih9gfDqlUKhwfHoDMct6osxMYuvJIJDnpDyiCcDF5wbyRF9gq5wkjszj2ul2asblWNpOh0+2yt7dHKZ9bymAz579YFWF6u/HEpSJFpVrBdV22ylsg4qSkBOiEzp3cE41lOxTLBcpbGhUO6fe71Op1VBTFPRRvgkFmkeRvTfPc9C2Oj48QY14/Yo1EaXaxeiNLQKc7i6ASozlDFe/R63VpNhuxjbM3U+YE422z7IhBEHL28AEHu7u43nxF8vS015iwlWNZVwiB67q4rovWmrOzMywpGQYhP/rXH7Ozs8Pe3h5bW1uPnHxghH4+/PBDlFJ4nkcURanbaYJ+rnKsdZLDpujnKiy1dUvyX9R47BLOUhHMNRJOr9fjzp073Lp1i5s3b6b73PRtZh7Cqa4opwkhsKVCMf8h7nY6NM/POTo+IpNxCAJThvADgR8k+zDlN0vqmCCwHPklJTAhSBcXgMtWi/OLC2zbUGr9QRY3XzQmWwtKaracP+szeY2T1OswMAhqq7xFvjAqNywu2wmjYq0EtqVRuDiuy5ZnfHQG/S7nFx38YZVcLks+n6eQzyGETGnPh4cHzPSBVqgUQGzWtkbCaV226HQ6HB8fz++rCUExn6cQJwjf9+n3+9TG1QPipLnMr2c49KnVqhweHJBbUhI117c6o2qAOTptRiS1Qj6fp1QqYXlFnrKzNJtNKpUK7777Lp7npYv1tNzQupFUFTqdDq+88kr6Hdqk97MoNv3+roN+BoNBSgNfJ77sbp/wGCacZbEq4SRvMy+++GI8xzL63KYP7LSqQW8IncHqhKOUnrWF1Jrz83P6gwE3Tk7IZQVBGEuR6OlNBX3fzHtobVCPSUAJApqa9J9eh7Sm1WrR6/e4dfOmGUrUIZ1un4vYC2bC/GzcEXSd+zKmMD0cxPTqvX2yY748EtaghE+mDK2NoZuTK1HOmfKnGYRsUWlUifwhXj7Lwf42WoupkZ/1xEPXSUoX502CwB/58swJrTV6TDQ1KXOWy+WUeNBut6lWzvDcXOqbY1mj/fX7AxqNBgcHh+Sc1c+lWEmriMkJU256ZrarQqkUl+uEQDqm5Lq/v8/+/j5aa7rdLvV6nbfeeoswDNnd3WVvb2+CkbcstNa89957BEHAN7/5zfQzi3o/48y38d7Ponv+qKW5eejnrbfe4oMPPuD9999fq/fzZPDzMYtFCUdrzUcffUSlUuG1116bqdcm8HkTnbRpVYOVZAGM10sQgjP2sqpjOq1lWRwfH08iODH7xq0x/ieJBpvSRkYnPYaEjG2ICTC5sCceNmjN0dHxSKXAtigWihQLxYm6/vn5eexr71EsukRqFUU0EYUUdDtdLloXHB0eYU/1XqwVCguQUMKXHy2TyeDYZTq9IVt7O4DgtNYl8H3cXJZCwaPgZc290GCsrvXcWRfDJlsmX6NpNBqgI+NjsxRVioWluYR4kM97WGJnbH7mLB6iNb5E7bZRD1hHEsc0sdZQmJ5CUwllfHt7O30zl5lZjyEhRKqr9/TTTxOGIY1GgwcPHvD2229TKBTY29tjd3d3ro6h1pq3334by7L4+te/vvTerer9hGGYbjO+8F/n4GeCfrLZLF//+teRUnJxcTGBfnZ3d9nZ2ZlYS57Qor+EsWlJLYoi7t69ixCC73znO3MfykdVKFAK6usknKl5kjAMOTs7o1QsUoqZR7bUqbLA9LWqWHFaxMIq8xbOSI003DK2ebN3LA1EVCoPyReKbJXL6dT/9ADqeF0fwA/MHErl7CEKC29sDmX6BJK+zEXrgn6/b+jV1tT9jm0GVt+r1f2iwE+cTffJZs0XP535GQzodLvUGhdkbIHnFeIeimXQYDwzJEUsUyMS87LZZ0trHUv8ZNje2ln5Rr8+FXpsUHbb6L01Gk16vR6WZXF+fkHBzcbzM0sW6bkWFNMnNZmUgiCgUq2yN9Uwl5nFfaIkbNvm8PCQw8NDtNa020bW6M6dOwAp+kl+Fz/5yU/wPI9nn312I2baOugn2S5JRNcZSQ9nUe/n7bffJoyVKT7++ONrG/z8r//1v/JXf/VXSGlM+v7iL/6Ck5OTa7iiR4/HLuEsi+nEMRgMeP311zk5OeHWrVsLH/ZHVShodsTq3gYaLew0gQwHsTT+/v6EPfV4SSpJOBPDnIiYCr1OGcPYVvcHQfwmu0MmmycIjSBoMoC6bF8ZJ0N2y0Fsl4kiUw5qtS5iy4Kccd50XdOg15pavQ6w0DrZtlbTqmF1g7/X63HerHJ4dGNmnmQ8aVpC48c+P7VaDaVVajI33ouwZWzdkCQj4hJbFPDw4UO2ykW2ysWVPZ51qdDTZAGt4fKyjdaK27dvIwQM+wP6vU6MNK1UumacradhrSHO8Xw1HA6p1Wojm4nk3G0HOWfYd1kIIVKyxLPPPovv+zQaDT766CPa7TZRFLG1tRVf06PRoJehn36/Ty6Xm+j/PGqsw3wLw5D333+f//k//yf/5//8H05PT/nhD3/IL//yL3Pjxo0rHfe3f/u3+f3f/30A/viP/5jf+73f40//9E8f+XquI54knLEYTwLn5+fcvXuXn/u5n2NnZ2fp5zZ1/Zz+zDrlNIMyzLxMp93m4uKCo+PjicVSoAnG0UYycz6WbBCztOp5kSClfr8f9wLM4hIpiMZUrDO2GUC1LSOiOU8vLElKUo4sC7TWDIcDut0ezfNzbCkIo5B8vsDO9s4SiZY17pXU062Gibi8vDRK2TduIuXyr4CUGsdxKJfLaQ+l3+9PzPzk81k8N2/KpGpkhmdKTnW2t4+QOZd+aGjcCTpKBDwTMc/keKvIYiYpjTbS2vQXkzmqZGH2vByeaxJCEIT0eqaPolQUJ1QP182uZNbpsZLbYDCgHqtWTCfqddDNqshkMhwfH7O/v8/rr7+e9nh+/OMfI6VMkcK4RcFVYhz9fPrpp3S7XZ5++ukZ6Z1H1XxbdY62bfPVr36VP//zP+c//sf/yG/91m/x5ptv8mu/9mv8yZ/8CS+88MLGxxwf0eh2u9c6r/So8SThjEWScD755BMePHjAq6++OoEeVn3uKsfqDTXt/koRrLgEJmi1WiilOLlxY+ZLMO2No9FEKqLX7ZnrMCr6aclt6flJuGi1abfbC9lUqZinAj8kvQbHiodQ46rdPLQhhCCXc8nlXMIwoPLwU7I5j+FwyIPTB5MoIj5dyeq+jNn5JK16PJrNJkEYcPPGEXoB2290jrOWDcYzJ5/W2geDAcN+m4cXl0adOaYvK6Wo1WqpCZwlR/bX89xZk+PZSiFELO0T2x3E01JG5FNM2iyYcl0Nx3HY3t5OyQ7G82b0TDqOPZY0dTp0Wq+ekctm41KnN/f3LCUQ6bQvd3R4ONuvlBKZuR4PmiAIeP3117l58+YETXg4HFKv13n//ffp9XpsbW2xt7fHzs7OlaycAT7++GMajcaEIoJSauIPkDqMXhf6mRf9fp+XXnqJ73//+/zWb/3WI+3rd3/3d/kf/+N/UC6X+cd//MdrOsNHD7GhD8T1m0b8G0cYhguTQxRF/NM//RN7e3t84xvfWPshvnfvHtvb2+zv7699Hg8ePCAIAkLnNh+cGYSQzUpsKxYbGWN3WVIThIpPP/mUTCbD0dHRXOVkxxr1bxJyQH/Qp9vtMugPcByHUjFHJldYem0CTbPZIAiWN7izjl6p52ZLjcYoTVvxLFByFIDhcEC1VuPoYJdM1iR3FSl6/R69Xi91C/U8j1LBRenlX3ZT+pnfR6nValiWxe7u7lqlOcda3QcSYlTeCkPj89Nut/F9P0VzuVwOx15dubLkaothgcaWyqAcFXH68AGlQp7tra2R7442tPeV/jmxmKfv+/R75n4DuJ4xbctks6Y0iKbTvuTy8pLDoyOseV5DOQ/bLS6/wDViOBxy584dnnnmmaXfJ6UUFxcX1Ot1ms3mhDfOun2QDz/8kFarxTe/+c2l7DUgLb2N/36S79Ciz/7oRz/iO9/5zlrnAvCDH/yAf/iHf1iLOPD973/fKKpPxR/8wR/wK7/yK+n//+Ef/iGDwYD/9t/+29rncYVYG0I9SThxJA96t9vll37plzaCoffv36dYLG7ke2PEAnucdp8yKgFjIQS4WYFjm/qX0CEff1rBtm0KxeLcaXE7bZKLCXJA+iho08Af9tu0O0MQiYNlfmS6hfmCNWunWI63tJSYvmmvuE7H1gTh5L0UmF7MoN/h4qLBrZvH2HZm/mOrDYro9roM+z0s21k4BAmQsWZVtJM5Ec/zYlrqWvOZ2HI1zXk6KbXbBhUeHBykwp2Dfo9sNkM+n4/lduYne1uqlcdLiCNRFFE5O6NULs88D8bqQMU2AaQlO3N7VaqfJnVkmGdapSW9KIro9/tpss9kMlgowjDk8OjIzOtMhxA4xR2E9WgFk36/z507d3jhhRdWlrHnfbZer1Ov1xkOh2xvb7O3t8f29vZMQtBa89Of/pRer8eLL764EWKZRj/J0PQ89LNpwvnFX/xF/uVf/uXKaG1efPTRR/z7f//veeutt65tn3Ni7cXySUkN43751ltv8dWvfpV79+5tXPO8Kkvtoitmkg2YxbA3MKWUQb/LxXmFmzeO8P3hQtkUSxoKs56XbAAEuDmHTGaXYtksLL1uj0azkTJlstksrYsWu9tF3Hx57nGSyNir0Y0AwnB2Gw3Um5f0ej0OD28TKslwEJfirHiRFKOd5NwchXyWSO0SjDfw4yHIhIIKM2MiM2rPsJ7ytbXGTA1MJq6L2A00oacnCgG21AyGMVuvUgFIk2bSdF9nhsfcDkNiqFYq7OzMVw9I9fQgfiMYv1Yr3Y/Enmi5CaERFmQyJTJlDVpROXuAP/CxhOSTszqFfJ5C3jV0a21ugLTsR0423W6XN998k6997WsTM27rhuu63Lp1a8J8rVarce/ePVzXnRg6vX//Pr7v841vfGPj7/o84sF4AgrD8JHKbtdRrnvvvff4yle+AsBf//Vf87Wvfe2R93ld8dglnOkH7PT0lA8//JBXXnkFz/O4d+/exvu8ijW1lJL6pYNc0iJqX7bptBvsH9wk1Dbt7hDL8vFyAXaMfjTmdT2IZskBM+c5xmCzLItiqUixVEQrzeXlJfVaHduCdndIpDtLXTfXQQiOrfGnEk4yj6K15ujoCEsKwghA4Ici7gWZEELj2PFQarybZQ38XNYiny/ieV7q8TLeRzFHmU1K80KuITI6bn9db9TRWs9xHDXltnGNupFdtZHRyeVyFPI5crlV9GUYDHyqterENc3GGvI6Y4rW6aeSJBXvoVE/R9o5bj59E4RJ3v1en9PzLlEYkXNzeK7Hdn5zk8HxaLfbvPXWW3zjG9+gWHz0stw4DRlIh05/8pOf0G63yeVyvPDCC48sADqPdp0QDtrtNkIIgiBYq/dznWKkv/M7v8O7776LlJKnnnrqc8NQg8cw4SShlOLevXv0+32++93vbjS0OR1XsabWWJx3bXbnJZxY6TkIAm7fvp0SAYQURErTHSQi9IqsA7msIApBC4FImAGzByRagEh6vR6dToebN2/iuRadrnkbf/jwYdoIz+fz6T1al1Y9/cY+7vmSvMVOEx0mb4PAD4xFwcA3r+LGwC1RRjDeMwlyCf1eqnigMWWnw4PDiYXZWqN3M48ssHA7ZWZsMtmMMY2bCmtO+c7YVRcnZn76/TbNZkJfzqczP+Mx6PdSX6NF1gBLZkYnYtk2Sb/LtgV7O3vp82Tb9sRLSn8woNvt8sFP37uydE2r1eLu3bu89NJLn9nQYz5v7meixryzs8PZ2Rnvvvsu+Xw+HTq9quROEgn66ff73Lt3jxdffHGi+rGO5M51JJ2//Mu/fOR9fFbxWCYc3/d544032N7e5qtf/erEL/kqumiWZeH7qyx5J6PRtonUYObnSikqZxWy2SzHJ4cTjLLk3MZj6BtI7wcmIeUyioxjGix6TAMnY2v86YSjx8pAJ8dYMa13fJgwaYSPl7C2Sjksx5vHWxjdk7EBVBiVtspTPYdpVeh5YVsjszmtxQxqQmgylsayPba2PKS8oN2+pFwqc35xjopG+mN5b3bgdOZ4YjUKEsKoMJ9VKkZlYcGbuWA53jC6aTnynlnsDH25R61WRSmdnncQBHQuz42Ctb24xr+W5ltsZT0vlFZUK1Vyrsvu9uK5ISGNqsH2Volnn7k9IV0TRVE6vFkqlRYuos1mk3v37vHyyy+vxQa9aiiluHv3Lq7rpsOjBwcHZsSg06Fer/Pmm2+ilFrrvJdFgtbGE+g6ZnOfJ+ryZxmPXcJpt9v8+Mc/5vnnn+fg4GDm35M3kk0TzqYIp9qyZr7MQRBQOTP9hkKxQM6ZlJ0RQqDHVhMdU2iDkFQ3bTDUDIY6Pq+IbEZgWyJmCY8WquQtVkrJ4ZEpAxm0MTVDY9vpYJ5SikG/z3mrzWDQjGdQzDDhdCloQhMtLm2NjMxMmIb78vusWT5TYzYyJcSBn9CeQw72b2NbAq9gehGDfofL8yb1ejim9Ta/ZLgOM0ZFPmdn1QlZl+kQa/Zlxo9o6MslyuUSSo2m0v1Bl2KpxGAwwPXcBc+nXupGmoRk/jVGyuiiFYtFyqUieo5Q53gIBBnHnpGuCYKAZrPJp59+yuXlJcVikf39fXZ2dlJkVqvV+OlPf8orr7zyyMhiWSilePPNNymVSjzzzDOT5y9EijSfeeaZueedoJ91nDsvLy/5yU9+wre+9a2ZZ2JR7ydZN4bDIf1+/5qu+vMbj13CsSyLl156aaEvSJI8NrGG3XTwszvQdAZyInn0e4Zlc3BwkApVTlNyU6kanSgHQDYDfjD/7SiKoNc3FNlIQ8bRZByTbM4qFQqFEqXymI/PipcsKSVbZY9CMY/WpIOb5+cXWJZFPm8a4Y5tp+im2+1yfn4+f1BQwKo0nYkN4paHJozMPIpl2xweHIAQRBqi0BB7RWaLLa+MHxpJm8t2h0q1iWNLioU8+WIBx3bieZnlRxsOh9RrZxxMleumw5ar54aWIRIhBH7gY9sWN599Ft8P6Pa6tFoXiLGZn+S+2nK1woJgPvU6jGJyRdmQK9aR17Gs+aUhx3EmpGsuLy+p1+t89NFHWJZFJpOh2+3y6quvztVOu65IbER2dna4ffv2yu0XnffHH3+MECItGRYKhRlE0mq1ePvtt+cmm+kY7/04jkMYhvzGb/wGzz///NUv9gsSj13CyefzSx/yR5WpWSdOG3pC5+yydWkGLE+O0z6JY8023FOpmjjZGOOw1VDccYw6gB9Ap2tsk3d3d8hmPXQYYVkCISFY4rMzHUJALpdLEUvCHqtWawjtk/MMIhoOh5ycnMyR+FhtVWA2XL2JFBGnp1Ujj1+ez65LrLSFEGSyHpmsR3HLnHe316P2SROtQkp5h2KpRN7NxTNDk8tuv9+nWa9wdHyy4qVkPXSzyJBOa0NEADg6PEAIyOay6ctIUupsNgzLMOe6FPM5srnlhm3zVCaC0EgX7e7spqWtZbYHSWQWGdqNhRAiJXk899xzfPTRRzx48ADP8/jXf/3XdHhze3v7WunAURRx584dDg4OUhuRTWL6vH3fp16v88EHH9DtdimXy+nQaafT4Z133uFb3/rWxqXBMAz5L//lv/Dcc8+lcjRf5njsEs6quGrCWRfhKK152NBIIVHaTKOrSHFycjyhsmtZgmDqNIQQhGGIUhohzZxOuMapJpeTOEomMjV+AH5gCAg5BxAKxxbIZPh02qpgiUrzOHsMHfDwrJ4ydJrNZmpXkCpMW5pwAVkgCSlWkxOCMKBefUB5e39p09m2mEsWmGS9RQyHfWrNLp8Om2QzWby8R95zcWxJr9Oi1TrnqZs3sFYstvPIArMxH20kYp9OxhARDBtucrvxUqdWiuGgT6fbpd5okHEc3Bj9TC/iQk8iF983LyDjrDczgLr8zKUQM6SGVfHRRx/RbDb5+Z//+fQ7c3FxQa1W4/79+2SzWfb29tjf35/roLluhGHInTt3OD4+vjbRykwmw8nJCScnJyilUvRz//59BoMBt2/fnpjLWfc8f/3Xf51nnnmG3//9338s+jiPXcJZx2b6KjM1636meQnDwDRnh8Mhnuexvbc1pRwwOyyJNppeQggenD4gm8myveViO/ml/SbHNg33y1aLTrc7X6ZGQxiZOZ6Bn0ipQMaBjCOQUqCFiJv3q64w4qzSIJfLcXx8PGFX0Gw2cRwzuFkuuiCWJxx7CYMNkt7QGQcHR2RXLFDrfJVzGYltFch7BTTaSP93jVW1UgohBIcHxwxUFmIncinMAi2FETNNhDvXoYrNK4EppalUzvC8POVyKRYOWKE+ICWFgoeXd0GPxEYnZn5cj1zWmTitwWBgyriHB2QmPC9Wn7sT927WiWTQstvt8q1vfSt9XqWU7OzspEOevV6Per3O3bt3CYIgdQxd5iEzHYkszu3btzcaxN4kpJRsbW2ldh2vvfYa7Xab+/fv0+v1JoZOF6G2MAz5z//5P/P888/ze7/3e49FsoHHUGlAa72UUfbuu++mTJV1o9/v8/bbb/Pqq6+u3PaNnyo+qRgbaBUpnnr6qZltso5JSuk5K5WuAYmnmj801snd3gBLSrx8nvyc6fuMozk9a6KUYn9/f+6DnbHAXyNfelmDvGwbw4Cb2lcYhvz/7L1pkCTVeTV8bu6VWUtXdVd19ywwMMOwzsL2CSO/GG0BAmaQDQgQQihYLGuXHJIsWcJCCtmyI+yww/5jybbCCjtsRzgAyX6tV5LtT0vIfj+QETMwwyzArD3dte+ZVbne78fNzK6qrqqs7plBEvSJIIKZqe68td2T93nOc065eAbx5PTIHplt2+gYLegGU+j1uh0MpniOs5/RDR21ag2bN2YBfnzTmePokAHIlRCHXI+CzQ25jgtFUdDtNOF6QCymQtNUyLKyQq3HAQBZNuoMHKQ5ErgAsDdz0FnAcdweJV8wpIoJuinLv3MQruuiY3RgGDqsboeJPPweQxhx3ePwzLQf0R+GuBYbanGzYmV+cJrjOLj88stXdfdfrVZRLpfRaDQiM3MAdlrbt28ftmzZMlQQdC7Rq7DrPY15nodarYZyuYxarRae2mZmZsJyW0A2l1xyCb70pS+9Hshm4iewTjgDWItNjWVZ2L9/f6SNhe1QfPf/a6NUYrMUhWIBmzdvXvE4RQRzIBjo1/S+q5JIYDvB73Vg6Dp0wwD1s95VTYMo8CgVC5AVlc29jPhgh9cbA1lEeL0AAg9IEjv5mJaFQrGMudmZ0BNt9O+isB0uHIDUDR2O7UCJKdBUzfceG61gY27PbczOzkKWuEhptTyBKwJP6IoSokc9lAJjzEzaj3bw4LhAp2NA1w2YlglZkqCqgW0NN5S4BrGcp+MPmdo2lpYWMJvLQVNjzIAUgDiJ3Q0ZH/4GBAVSD91OF41GA51uB4qsrLhRYeW08eVhgeehqdElr97gtO3bt695Yw3ky6VSiYXYASsa+KZpYt++fdi6deuqbhbXgkqlgldeeQW7d++OVNgFKsNyuYxvfvObofv6Nddc83oqo60TzihEEc7x48chy/Kqar+O4+C5557Dm970prHX/e//OYXDx7u4YMsFILyIU6cXVhAORyib+B5DNgAgS0wEMAjX88JBTrvbgqiwwDSlp3/SC0JGOzr3Iib1n7p6oRsGatUqLtiUgyzLEATC7FVIj29KcD0sW6/0glIaenh1uh3EJA6KlmR9CI6VJSgoqtUqHNtBNpeFLABOhJknKLPLiRrklIT+uaFAIhzX4qHdO897Q9aNMHWz0zFAOA7JuIJYLD5WVCAJy55vYb5MNgdJXr575wkFCPrLdYSZaYaeAMSDMAHh8P7sTbPVhN7WMTs7ywi/Y8DQDX/GSkFci0HpcegehpgiRwoGPM/DgQMHoGnaqoPTohBk5pRKJei6jng8jkajgUsvvXRVBrprQeBWffXVV69aYVer1fDhD38Y+Xwe3W4XW7duxX333Yd77rnnPK32NcPEb+56D2cA50OlFgyenViUMZWeR6vpgBAHlmGApw4o4eD5Q5qSQNC1/HmKEWTDcf0WMH1r4TgIggDHcbBx8yZYFiOESqUCUZKg+c1kzq8tS8JoIgmvRzDyeo1GA7phYH7DBogix+aGrGDz8yAK7DkFSjgmdFhJEiweWfUlpRS2bULXO8gv5dmQYUxFp9OBJEvIzeZAQECIF3kLJArDxQL96DfgdBwH+UIe6al0nxCBJwTOwPWYWk+GosgA0qCeDV3voFwpw3XdcHBTkZfVY7RHwRbc8Q6VjXNs7S4lI4tcPMd+ESvV+X5oASmRZdNOj7qo12roWl3Mzc6B49jEe0pMIZVM+TNWBlqtJsplkwkmfKFHb+oqIQRihFjAdV288MILyGQyuPBsvT+aAAAgAElEQVTClSXjs0WQmTM/Pw/DMPCzn/0MqVQKx44dw+nTp1ftGj0pSqUSjh8/viaysW0bn/zkJ3HNNdfg8ccfBwAcPnwYp06dOqdr/EXHG45wosDzPGw7YgcewDgSC+rKiVQOipbpCUUDTBOo19lpS5Y5yDIPl3C+jT0ZSjYA20SHnW4ANtjabDaxccMcOF5ATCCsZu+f7HRdx1I+D44QqJqGqWQMIOO/PJKwknCY11YZnudhfm4OPD+MBFnZj5Xi2MYYk1gcMzsFBU+wn4AkASBEgSQpSKfTsCwL+UIehBC4hosqqtA0FRwXXdaZ5NZL7FGwWRbzKpuZnhlQSkVHFQBMKswHg7KUeb21W2yaPdjEE5oCj/LQ2zrqjTrmh7kHjDYD6ANPKFzKaMWlGJoDxBGKarUOz+UxM3MhOh6r2DFiWiYpRZOgaCkQUHS7rO9TruXBE+JbCKmIa+rYz3ugEJudnV2THHk1CAw/d+7cGZ5CA9foI0eOwDTNUHgwNTV1VsaYvWSzmhk9gJHNo48+ip07d+ILX/hC+PpdfvnluPzyy9e8pl9GvCEJp3cGZhA8z6PbXWk5sxa0Wi28+OKLuOSSS1BuJUEwupRnmh4cx4VlexB4glhMgCDy8IaEhA1TYFMAtWoVlm1jfsMGqDJBt3cglBBIsgxJlpEG2xi6RguL+TKzflFVaGHg2WDjfPD6HgrFImRZxvTMDAgYCZojBlAD8BxdfowV+MEBHO9BFgCBJyA86Zstsh0bxVIR09PT0FQt3MSNdh2VigNJkqGprBE+uKFwWBlVMAzB1TqdDipVP91U7CdhdlKK/j297w1HOGiqBk3VQEFhmRZ0Q8fSUhmuXwrM5XJDrWoEfhI/t+hZH0opyqUlcLzYV27y54f9kRzChoN7emZETEBLJaClmJjBMAzUSgbMV19FOhVHNptdsYkHCrHNmzezzKbziHa7jRdffHGF4eega3S1WkWhUMCRI0egqiqy2eyqfdOKxWJo8LsWsnnkkUewe/dufP7zn3+99GzWjDck4YzDWpyfh6FYLOKVV14JXQ2ef1kf+rig9k4phcwR2CBwPaCtOwAcEACKwkGSeBBOACdwK2ZvvGBuw5+UJojeHAVBwMx0GvFkmrkuGwYazSYs02TWL5qGmKJAFLk+sUDgiZZMpZDoUaJN8pKNKt95LtBx2ash8OyOXeAoXKeLcrmA+fk5KDFWHgk28amkCsdl/Q/dYNJljudZydA3GhWE6FkfQhgptdttNJoNzM3NQRhqte/XN8dgnKqOgPgedRLqxINl2VBjKmq1WhgPoaoqFH9wkxBElwsjelPU81AsFqDGZEwNMRbtxagBVAAQBB7JZALT6STSl+RQq9VQLBb7NvFEIoFDhw5FBqedCwzzKxsGnueRzWaRzWZBKQ393lbjm1YoFHDq1Kk1k83DDz+Ma665Br/7u7/7hicbYJ1wVoDjODjOiIbFBKCU4vjx46hUKrjuuusgSRKqDRdtY+WOHHqjEYB6LGJgcE+jADpdD52uB8BGXOVAOA6CyIOCh+16LIgrmQzv9ILZmygExMVxHLR4HFo8vjw3o+tsYFMhkBXWvHdcF8VikUk8e8pNwoTXi+6l+AOaDtBsGajWapib3QjLFWG1PXCEQhIJRIHl7BDib+KKAmQycHqzclwXcU1GTE1AluWRX3aRp6hUWzAMA/Nz80PLLpNEFUwCCopaOQ9wAuZm5wACJFNJ5rzsRz5X/MHNeNzvtXHj+iWjSZCFzuWR1GIj3Rd6f88krggxqd/6P9jEl5aWcPjwYSiKEtr/D7N/ORdYjYVML4b5vVUqFZw+fRqtVgvJZDKUXQeKvXw+j4WFBVx99dWrdpMPyObaa6/F5z73uXWy8fGGJJyoktpaTziu6+LgwYMQBAHXXnttuHmdzg9vuBBC4HrMKFSWh6vO+h4PZs7JBAouTNNEo17Exo1z0BIqXEJBKAHPRQ9oisJKmXOwplgshlgsxl4jz0Kz3cHi4iIcx0EymVwxzCZwiHQ8GFSBDQMFGz4NhlQ3zM+H4gaA3c13LfZI9lqx3oMoMKLieQ7JZAKpZBIgLnS9i2azCdMymQQ4aIL77wub6K/AcVk2z6hNQRjjsBAgipQ8yqIZVEXE1NR0H08QjkDVVKiaClDAczpo6R0s5VnfSvVnfsSeMt84DzbXdZHP55FKpZBOqdGnXW6C4VJCEJNW/h0hBJVKBddeey1UVUW5XMaJEyfQbreRSqVC085zYVtTq9Vw5MiRNVnIDEIURczNzWFubg6UUjQajRV+b4Zh4Jprrlk12ViWhYcffhjXX389PvvZz66TTQ/ecLJogN19jCKVVquF48ePY+fOnav6nf/1X/8FnuexYcOGPqNAz6P4Pz/RYVr9Lx0FM5t0HQeapmE6o8GK8DJTJALTbwMNM8XkOCAW4yCKPMAJofJt6O+aYPZGEhiRNJpN6O02ZmZm0DVN6LoO13HCvo+qKpH9BkWiI01GA4gCRbFU892es31WP8ugEHgSWcKLyawrznMEhKMwu13ohoFu14QgCIjFYjA7bYiygkxmWcyx8mosfyfq+Y2bvQkk1sl4DMlUdJqlwNOwj+W6DnTdgNExWOlNUaCqGhKa1Bc/EcBxHOTzeWQyGWhaDNwEX1mBG26x0wtFIkhr/c9vXHCa53nhJl6pVIYOQK4GwezLrl27zsr2ZhKcPHkSCwsLUFUVpmliamoK2Wx2aFz1IAKyedOb3oTPfOYzbxSyWZ/DGYdxhGMYBo4cOYKrr7564t/XbDbxzDPPYNeuXSsmnJfKDv7vvn7bcUopPMokvbZj+7n3OjzKQQvCzobMOagygWFSNOoNdDod5GZz4YxKAEUGur7tiiAQxBQevMCDBumgmHz2RhEpFgtVuK7LCKDny+NRio5hwOq2oHccyLIMVdOgxmIriIKAgufI2OtRSlGrLoFwjABGDalOclIihLnmDM7MAL4fnNNFsbAIkaMQJBmJeBxqPA5Jkoa4HXjRzXvKgt2GXc9xGQGkp9JIJ2OR0dYCofBGkR/10Ol0YRg67K4OUVb6ZO62ZaFQLGBmhnmRiVx0XAEhwadi/OPScQJFXF5XUNrasWPHRMFpgW1NuVwObWuy2SxSqVTkphwoxHbv3n1e3aUB4MyZMygUCti1a1dY7eh1DlAUJSTOQeKzLAvvf//7ceONN+LTn/70G4VsgHXCGY9xhGOaJl588UVcd911E/2ufD6PY8eOgef5oZPHz77YwUKB1a4oaDjQ2RsDrUhs9oY5AHeg6zo812UnCE2FLMnh/lsslUHAJq2HfaAVmYR5OIOQJA6KzAQINuVXTNb3gXooFQsQZSZNHvVIWQJMC+iaJgxdh9HpQOD5cIKdFwTfWWD0tVzPQzG/hHgyjmRy/AlAEVe6aK9Yk0hhjRALBKKHqakkkokEHJcNynaNNlzHRDyuIJlIQNMYcTLHgwiS4IafgCw7cOaeRkxR/AHUsb/Kj2OIvl4wwKwbBgzDAKUUrutgZiYLTVUBQiZyKZiElDiOIJdclv8Hti5rLW0FtjWlUikydyZo2u/evXvVTfvVYmFhAcViMSSbYQiEB+Uym7NKJBI4c+YMbrzxRjzyyCP41V/9VXzqU596I5ENsD74OR7jPgyTDn5SSvHqq6+i0Wjg+uuvD5MOe2E7FEvl8WTTC+YAnEAymfCVYx006g1YloVEXERbdxBPJJBKJYeWgDiCFaW7XliWB8vyoCguTBOQZAJZ4sHzHDyyTECO46BaPgMtnhmbMU84fx6IkDCqIAPA9jfCQrEIUIqppAJJSUCUpBWrth0HhXwes7kpSMr4PHuORFvUABhJpIEz8vT0NKYSCmyXDcom4nEkfMFEp9tFsaKjc6YKSeSRSGhIJjRIIu/HWi8/d0qZmmyYoqxrdpl7QC4HWZInOikRRCeNBq+Di2WZu6IoKJfLSCVTaLdbqNVqUBUR8Xg8VL2Nfq2iEZOWvzPnIjhNEATkcrkwdbPVaqFUKuHUqVPgOC50jG40GlhcXHxNyOb06dMol8tjyQZg8SaapuHCCy+E4zh45ZVX8Nd//df4rd/6LczNzWHjxo2o1WqhIek6+vGGJJxxmIRwgmAnRVFwzTXXgBAyVGywWHTguj7ZeMx+ZJBsRpEEU45p0OIaLNNCtbwEXmAqILPbhaZpiKmxvpKaJI0+3Sw/P8D0H2OZFJYZrJlAlgkoZXMvGzbMQZSHG3CG1+MBc8hpQ5QkTEkS82+jDnS9g2qtBse2ocRi0Hz5r2lZKJVKyGaziGtypIHosAHUQXAjBBPBRH8QzTBsq2UN+hjUWIzpvzwTzXYHC2cKAJgTQm/znhAKkQccgQ1gEt/PlDljVzA3Px8aYwaJrOPAjzgp9a1xQFGm6zrq9Ro2zM+D95vb1PPgmDrahu47TIjQQq+35c8LT6J7NwBCsUA+n8fp06dxzTXXnDMCIISEMQtbt25l4Xa+dNkwDMzPz6PZbE7UP1krTp06hWq12udkPQkEQQhTRD/xiU/grW99K77zne9gz549+Iu/+IuJzHzfaHhDltQcxxlLKv/93/+NG2+8cei/dbtd7Nu3D5s2beqbpD5w4AA2b97M8mB8/ORnBgpVZyTZAEBM5tAxR3fAO0YHtVoZM9lZyJLMBggtC7puoGMY4HqcojVVHHvCAQBVIeiMICXD6KBarWLDhhw4XoYsEcgyB57nQAm3okktCYAVceLoFQt4lKLb6SyXgTwP6UwGU8m4f3SILpWNK80BfgLqwGPa7TYajQZmZ2chCIJvUBl9UpJEhP0i12WBZ7pu9M3NpBISHG95Ew+uNTc355+KmJebwGP5NERoGIvdi0lMP8Wek1Kr1UKr1cLc7Gyfmo+A+oaeDJZlwfBfcwChhZCqCJFuBqJAMJMgWFhYCHsbq1VtrRbBaeOqq65Cs9lEqVRipzZVDfsn5yqW+uTJk6jX69ixY8eqCc00Tbzvfe/DW97yFnzyk598o5XRerFeUjsfqNfrOHjwIK644gqk0/2DdIMno47poVB1WI4KyMgP47j6ebPZQrvVwpYLN8J22IZCQCBLMmRJBtJpJjrQDVQqBRQK/maiqUMb4MDogVCmRNMxPz8HTRXRtVg4m2UzCTbAnAAUhREQxxOmqov4kvW6BnC+X5rtOLAtC1PpNLqdDvJLp0A5pW9ocxACF002wMoeSaPRgK7rmJubC+/uBX64JLwX/EBAHM8LSCSSSCSSfvO+A11vo14zIEqMfBzHQafTwfw8m+dxPTZ7xBEKfYgCkRAKwS/T8RwF9Qg4LgjwCp5I/3MO/tSo19HpdjA/N7dCpDEY/iZJEiT/xBk4dNdqVVQcC4pPnDElNvStVKXl4LTdu3ef01TOYThx4gQajUZ42piensb09PTQwc2AfBKJxJo2++BaayWbBx98EG9729vwiU984o1MNqvCG5Jw1vLhWFxcxMmTJ3HNNdcMbZT2hrBRSnHsRBuc2wXhxZFlEoEnw08klMlAXdfF/Pz8CHkwgyiwxMq53BTaHSY6qNfqsGwbsZ7yFTNdJH7CZ9+lwmvNzc+BI2QkKTkuRVtnBBSTCUzHDy0TCTienYB6T0Es1XP5uVOARSIHz8svYYlCBl3TYVHPxSI8SqHGYstx4IRl8ETNKQn88omEUt9Z2nHCawWYZMxqHCkRwkFVNSQTKjzKrPErlQosy4Isy2i1Wkxp6BPnaNWZn+rqBuq74aTEc0HIG0A9gmq1DMe2MT8/x/KRBlImCRmd2MnzPBKJBNJTcXguRafbCaOqBZGV3lhSKFvL4sJxGHp71eWm1SIYmG6320MJYNTg5smTJ8OZn0B4MAkpHjt2bOS1otDtdvHggw/iHe94Bz7+8Y+fF7L57ne/i49//ONwXRePPvooPvvZz57za/w88IYsqbmuO9ZNoLekFgRI6bqOHTt2jCwnBDk6uVwOnufhf/97AdWaDRACWeYRi4kgggCX8uGLqCocjG7/7ud5HooF5lOWTqchigSTGB+IIoHdQyaB3T+bPelCliRkMip4QQNHlktcxWIRkij5eS9+zk7UgCalbF0rqpIEskQgiRx4nkCUOFguBwICj1KUikUIoujPvfjrFrBCleW5LowOU+vZlgVFUZBKapDk4RELAYJyGqUUpVIJPM+za/X8jCBQeBMMoEoTuEwrEoVpM8t6QghmZmZ8paHBlIaeh7gmQ9XGux0Ak5XTJMFDvricB9NHMr5btCD0RxkQMAJi1dxlOcWgOo0CsC0buqGj45fePMeAhM6aNuXVgFKKV155BZZl4Yorrlj1Bt478xOkymaz2ZEzP6+++ioMw8CVV165JrJ573vfi1tuuQUf+9jHzgvZuK6L7du349///d+xadMmXH/99fjHf/xHXHHFFef8WucI6yW1swWTmTKb9UQigd27d0eq24LeULNlh2QDAKbpwjSXy1KqJkIQRThO/8vv2Eyym5qaChMfRYHAGfTEH4AooI9sgH67/zAu2TDQajfA8zxiSiy8M0wklsUBAk8iXQpGuyJQmBaFabF7ekHgQCkbZCyVlpCaSiE1le67a+F5rDDY5Hg+vJullMK1DTRbBjrlKiRRZPM+qroicdJxA0uXAmKxGBMtDEAgGGOhyiCNCX/rfa62Q1EoFKEoSngtpjT03aI9D66tM7cD04Qsy0zs0eN2ALBZn6jrUUqxlC9AENmNyOBnMXCL5in1+2qjP6scx4inL86AAITnEU8qSCQzWMovgfNMgAOeeeYZpNPpiYcfVwNKKY4ePQrP89ZENuz5cEin02GZO3CMPnToUN/MTzKZxLFjx9DtdnHVVVet+loB2dx666346Ec/et7KaM8++yy2bduGiy++GABw33334dvf/vYvMuFMjDck4UySidNut3HgwAFceOGFE4WxcRyHTqcDz/Nw4nR3ZG/DcSmaTQuy5MCyPaiqCEkW0LFcFIoVZLNZyMpyQ9SOIBuAkdK4xxEQJBMKbEVBKsXycYITQLPVhOMytwNRFCNVYADAc0N0wANgAXEUtm3jVKGIdCYNQEWj3oUgsFOQKACuLYCw+/PhaycE8bgKSdZYtLZlwdB15JeWQDgu7PtoCo+O5fVENA9T2E0mq+a50WXF8DHExZnFIhKJxEjpOMdxkLQEFDUJShnpBw4RPM9D84lTFniMu5xHPZQKi1C1+FAS7cUkBQuRY6dKb0icAaUUxVIRihTDNbuuAseRcPixVCrh6NGjoWHnzMzMWQ1i9iaCXnbZZedsAx90jK5UKlhcXMS+ffsgCAK2bt0Kx3FWpbTrdrt44IEHcNttt+EjH/nIee3ZnDlzpi+YcdOmTXjmmWfO2/VeS7whCScKnudh//792LFjR5/qbBQopZiamsKrr76KZ599FgdejoMixiaRR5lGCsymRtdtFAo1NBoNbN40j5gIcMSB4wnsJBFxO05DX7HxEHhWcjM6HdSqNWzYsAGSKPpN5A6qlSoAC5KcYMOmI0pABNEWNQAbFgxnUbI5yD1Jlo5D4TisD9TU2ROUBAJRIhB4DoTnWOop4UDIsliAAJAlCbIkIZ1Ow3FY36dcKqHsdWG57E531OS7LER7zIFEP8ZxHBRKZ5Camhk7ZS+Jy2U50jOrBLDhY8MwUCwWQOAh5scYSHK/2MP1XBTyBUxPxaEmxpONwE3gigCMJDePLp8Ot2xIguPYI4c170ulEvbv3w9gZdzzJAhCCRVFwdatW8/bBh44RtfrdWSzWWzatAnlchnPP/98OPMzM8Pex1Fr6HQ6eOCBB7Bnzx586EMfOu8CgWFtjteLKGGdcAawsLAQmvZFkQ2lFJ7nwfM8aJqGXbt2oVI1sf/oKeh6G+VyBbIsDbV8MS0PoBS1Wg2maWJ+fh4e5dCosyweniMQUhJ4jgclArwRUcqKxEVKoVmpi6DZbKHVbmF+flmxxZrIcSQSccgSUGt00Gy2YJplKIoMVdUQiylhGUWSOJj2+OsRANVaG9VaHXNzcxAnkNFaDoXlUPRuh6JAoCocKM+BcARBuHIAQRCQSiahyCLK5TKmppIwTRMLCwssYmHArHOSSjPzjxv9QNu2UCzk2UCnMn7KnpDRbs6iyMQeM9NJWDYb8q036rD8npWmahAlEYVCAempKWgJLbKBynMkMv+n16etF57nIV/IIx6PI5lIIqkMP+r2Nu8vuugiWJaFcrmM48ePQ9d1pNNpzMzMIJPJjCy9BfHT8Xg8LBudLwwr2aVSqb6Zn6CnM6xs2Ol08J73vAd33nknPvjBD74mG/+mTZtw+vTp8M8LCwurirz/RcYbUjTged6KVE/P88KUQEIItm7dOqIsw9BLNoFrLgA8/2ITLx5uBQ/qs3wRBQGqpiEzFYdlLze2p6enV5yECCg4noPrj57LMg9FEcGLAhzKI9jIYgpBpxtlvAgs5pliK5vLhqKBgQuC47iwJMNiCkwYho5OpwNBEKFpKjJpDXZExozZaaDW6GB2dnZFnyUAG7shkSUgRe4nOJ4jLKJAZImhum6g2aoiO7s5FHSEEQuG4a9dQEKLQY3HV3jPDUIW6cjnZ/ontk0bs+D48QaSXKgYjxICDCj5/LW32i20223IsozMlIaYmohQX7F5n6jXUxpi1eN6vrt0kpUiZZHiwunVxawD7DtUr9fDuZlYLLZibsbzPLzwwgtIp9PnJX66F5RSHDlyBIQQbN++fSxZDHqmffOb38S2bdvwwx/+EHfddddrRjYAO0Fv374d//mf/4mNGzfi+uuvxz/8wz/gyiuvfE2uvwZM/MK8IQkn8KEKYNs29u/fj3Q6jYsvvhgHDx5cMcQ5+PPDyAYAnv5OHi19yJeVUli2DUPX4dg62rqDmBrry9/oRUzh/AycleAIEFNFSLIIwgtwxjScPeqhUSsARAmVaMOgKFzoRD3s+dq2jY6hw+gYoAh6J2p/HZwClWoVPLGRzsyO/YIqChl5vQA8N1pSDLA5Jb3dxgUXzIHneIgiB56Hf5IkYZqlbduwuy00deZqGvR9pIEaPs8FH/CV12TuAVXMzc1CjYmRcQyySMe+L+wqzJ1gsI9iWiaKxSKy2Sw4joPdbaGls5Ov6pu7iqLY9/qKgjf05DIIYcBkNDQXTaehqaw8mE24SGtn91WnlIbZRGU/ijyTyfiv4Vyfo/r5AKUUhw8fBsdxkWQz7GefffZZfOlLX8LS0hKmp6dx66234u67737NGvff+c538IlPfAKu6+Lhhx/G5z//+dfkumvEOuGMQy/h6LqO/fv3Y+vWrZidnQUAHDp0CLOzs0P9kAL1WjD70PtBLlUs/J//tzT22pZpolIpIZGcgue6TD5LabiRSKIIEAItxkPvjN/V1BiHTpdCEDg/klqAR/iw/Oa4DoqFQl842yjEFM7PmhnzGJmgY1G4jgs9kP76JqNqLIZGowFZEZFJT4//RVh5chn6/BSCzrA1UaBaq8G2bWyYmwEdEsMNsJwZSWBqOUkCQDg4rgddZ7MnTk/EgqwoUCQKe8iAZrvdQrPZxOzsHCSxv6w3CrK4Uu49CEnwVszedLtdlMtl5GZZzDXnW+YAJBza1HUdjuOw0pumsd6QFO2iPRizYDs2CoUCpjPToXyYEIqLZlwMSb0+K3Q6HTz//POhBVSv5f+5HiYNxAiiKGLbtm2rPpkYhoH7778fd911Fz7wgQ+gXq/j+9//PmKxGPbu3XtO1/o6wTrhjENAOJVKBYcPH8aOHTuQTCbDfz969GhYzx38uWB+Z1h9+qf7Gjj0cnvkdQ1dR7tVQzqTg9ij7vF6NhLbdqCqLDFRkuSxk/xqjB96CpJlHoTzUCyVMDc/B0Eabx/Pnkp0cooiEXQHSMLzPOhtlg4KQpCZikGUE4iNMY0UeMCdoLktS2SFao5SinKpHDayVYVEEqUg9DseEEIgimyY0ux2oBs6TNtGQlOgqEmoagyE7fJoNOowDFYe5DiOWfVEOB7wHIXPEmMxOHtjGAaqtSrmZufCU68kDpdMB3NWLNrCgKKI0LS4nxI6/Nq95TTLtlAoFJDNZqHIy+VBVfawKX32Eeu9sG0b+/btw+bNmzE3N7ei9KYoSqh6O1vLGkopXnrpJciyvCYxQkA299xzDx577LHXTbP+PGOdcKJw9OhR5PP5oZECr776KjRNw9zcHIDxJbQAlFI8+b8LMLrDy2mNZhOGruOiLfPoWqPfH+p5oF4XlZoOs2tCVmRofvO7V3TAsYm+oTX7oPyTy+WQTCkghIMsC+D4/sHTAJOcbnhuuJOxbdsoFIrIpNOIqTFQ10S9YaDT7UASpR6T0eW1qwqHToTQQRgyeBkMxSqxGKZSKYAAsshFSscnJSWjY8HstmF2O5Bkng1Q+qF6jPgniytQRMCOeMygn1uvB1vvHb8kTuCvJnjodm3oOit5coQLZ7CCkichbP4GlIQlu8DJuhdzKRfJ2Ln7mluWhX379mHLli0rsqICBKq3oPS2VssaSikOHjyIWCyGiy++eE1kc9999+Hee+/Fo48+uk42k2OdcMbBcRwcOnQI27ZtG3o3eOLECYiiiI0bN05ENgCQL5r4/o/KK/6eUopKuQxKKWZyWQg9QoBRUGMcjI4Xig50nTXuRUEIZzcScWmFSwHAwuBarTZmZ3OQZQGe1/+mEQCxmABJFsHxPBzKQ5a4yPmb2BDTT7NrMrfnXBayLEMUCAI7uWBmRtd1dIyObzIaJISKkV5msQGSYLHJBaSSScT9QdUoRVkAUVxe17jrmb7cm1I20Om6bmgdwwQTKmKKAl4g4ILPAgniEHr6KSIi+ymysDwT1Gw20dbbmJud6/s8spNS9PNjJ5flP7t+qdYwDDiuAzWmIpVQIMoxmF0T5UqZuWaL/TM0HEdxcdZlNzPnAJZl4fnnn8fWrVsxMzMz0c/Yth3mzbTbbUxNTYWqt3GlN8/zcPDgQWiatiblm67ruIFCTocAACAASURBVO+++3D//ffjkUceOe9k88QTT+Cv/uqvwirKH/zBH+C22247r9c8j1gnnChYljXSmv306dOglGLz5s0TkQ0A/N/n6nj5mN73d57rolAssqn3VAoxhR/rDA0EJ5chfl++6CDYSGIKB0HUQs+uXu+woNmsqj5xjYEkchBFAaLMg+MEeENcodnjiC9bZtB1A3U/4jpIJ1UVEqaNDsJ2HBi6AbPbhuP5Vv+q6nulrXy8KHJwfGK2fQeG6elpxGK95Z/ok0uv4/MoUDDlm+uxSHA2i6KEaZRB78S2WuiYdIVHHcDKhILAekYcx7GKmn8KZVkHy68ppZQNvXrMENY0TeRyOXADZTgmPBi/9sA1YORz85v3VrcFo2vBdV1MZ6YRj8dX3GwlYx7mUuemnBa4qm/fvn3N2TBB6S2wrAnSNrPZbF9VIpBZJxKJMC5gNdB1Hffeey8eeOABPPzww6/JyeaJJ55APB7Hpz71qfN+rdcAE79g63M4Q8DzPLrd7khxwCBcj+L0Qn+MNCs1FfoGEbkJbh0VeaW/GgCAkND1d2Y645OPgWKxBM/zQCmFLEvI5XLhWicxqRRFDoZhA4YvEyeAogiQZQG8IMAFD0HoJ5tGg5UH5+fnwfHLm9Y45ZYoCEilklBnU9A7LGWzVq/Dtixm9a9pUBQ2bMr83Nj1glNULpeD1DM8CjrBECcAnh/m+dYPWWJrd10P+XweyWS/e0BgeCkISbgu6520dR3lSgWSxMqGaiwGx+VACGD2ydQpiwvgXQg8Ac8xYnIdoFQugVKK2dxs2DNa/ikamdYJME+0caRECEEyoULnga5Vw/T0NMyuicWlRfA87xM/u2lJKufmfrLT6WD//v247LLLIp0RxoHjOGQymZCwArfoIOwwGEY9ceIEpqamsGXLllVfo5dsHnnkkTWvdR2TYf2EMwSFQgELCwu45JJLJsprP7PUxX/+pBL+udPpoFKuhKUmYMzJZQBhOW0MNJUPH+O6LpaW8pAkEZ7nhVktyWQcoihH3nvIEg/LGn+9ZFIE4XhwPI9ytQbbBbK5bB8JS0L0xs5MMTk4PTspa353Yeg6ut0uJFnGdFoFJ6rodrqoDZyiwnWLJLIsB7DNPeo1j8kEepeV7NgNgrriMcNOShRMdRjk+/Ach1RSg6LGx2bGyKKHxXwFHMdjejoDgEUY8DybMwoydAhP/GgLsH4d0OdCQCmFJA4f5OxF12ig3myz/lDPHFIQbWF0DFDXwsZkB7kc8xxb612+YRh44YUXcPnll0/k0rFWBKW3l19+GZRSZLNZZLPZyNJbL9rtNu677z68973vxcMPP3ze1joMTzzxBP72b/8WyWQS1113Hf7kT/5kReTJLxHWS2pRsG17RUJn0K9xHAdLS0solUpwHAfT09PI5XIjrTs8j6JYtnB6sYsDh/IoFJqYnc2FCYwAU5QZETJnjiMAjb6zVf3SXBCZnMlkoKqqvxaW1eK6BppNX3TgG0YOrl0SCewJbHEkmYdpuSgVS74T7zSTYUs8QHh44JkQICJtdJjqrA+U5Yx0TQPNZhsepUhPTSEej4Mf0OmqModuhPBAiboeABACz7WxlC8im50JrWdW/K6RhqXL4GCj0WbkGUQsqJoG2Y9YAJgopFwpQJZjmJoavcHEJApryABqSEyEmbZyHOsjMXdo//3tGThtNpvodJqYm90w1nQzqdggZhGlUgmtVgupVGpNG/iLL76Iq666KlKGf7YIjHVnZmawceNGNBoNlEolVKtVyLIcqt5GvZ/tdhv33nsvHnroIbz//e8/L2t8+9vfjnw+v+Lvf//3fx833HBD6Pj9+OOPY2lpCd/4xjfOyzpeA6wTThQGCWeUOCC4kyqVSjAMA5lMBrlcLqzv9/78K6+8AsMwsHHzpVjMMwKq1NguNQnhaCoP3Rj/GIFn6q1eJdowA0VZ5mCaHrrd7rLoQFrOO+F4DlpMiFyTLHPodF0UCgVme9IjHw9ACIWqihAldgqiPbNAvWBquGiSyBdrsCwL6XQ6jFhA76ySLILnJji5TDBcSt0uFgtVzM4Ofx3Z82Mbe7QrAlgoHZYjFgxdZ3Y1sRhisRiMVgWxeHro6xheD5SdzCKk42xuaPRjGo0abFPHxk0bwfMEPOlNHV1uMYEAF067UPw52MDuP9jAR/VOetFqtXDgwAHs2LFjrEPHuYDruti/fz+y2WyfyWWA3oHToPQ2MzMTntwCsnn/+9+Phx566LyudRKcOHECd9xxBw4cOPDzXspasU44UeglnEmVaK7rolqtolgsotlsIpVKheTz0ksvQdO0Fdp/3XCxsNjBwpKJfNGEO+b4Ms5dIICm8sgX6qESbVjpRhSWeyAh6LJqzOgw1dhUSoMkqWPLP5Lk4fiJfN8pahCKwsitF4LAQVF4CKIAwrGIasLxY09vlFK0GiXYLs9UTT1vQ2Ayqus6OGpCVBLQVA2yIg/9tE9CErphQG9VMJPbOPY1mOSkFF5vyGoopTD8/oMoeBDlODRN9WdmVp4eJnUpEHgy9PWkAGr+YOwFG2d8K6TRUCWKKzePvvEIeielUimULWez2fDE32g08NJLL2HXrl0jPyPnCgHZ5HK5voj3UbBtG9VqFaVSCX/4h38Ix2HOCo899hgee+yx87rWcVhaWsL8/DwA4E//9E/xzDPP4J/+6Z9+bus5S6wTThQCwhnnHDAOgYJmaWkJ+XweiUQCF1544UirGgCwHQ9LBRNnlro4s2T2zewIHFMtjX2BKYWu19HWLaZqGlEiUdUJyndwUW/o0HUDlFImWR6we+l2u6jVK5iezo0dyNMmuF5M4eGBQJZ4CCIP8Dy8npkg6lEUi3nE1BhSqfTYj7AsUtQbXTawOZgz479/USWwVquNVquB+Q0bIktGk5TTFAlDS2AAwk1uejqDeFyFaVrQddb34bggt0gLZ2ZiMg1PSqMgiRTuEPVdkOBKPQ8z2RlIIhdZot2U8TA/4bBn74lf13WoqopWq4Wrr756on7n2cB1Xezbtw/z8/NrMrOs1Wp46KGHoCgK8vk8Zmdn8eCDD+K+++47D6sdjwcffBD79u0DIQRbtmzB1772tZCAfgmxTjhRcBwn/A8Y7hwQheDO7rLLLgPP8ygWiyiXy5BlGblcDtlsdmSZhlKKas3GwlIXC0tddE1vbDmNeh6q1SIIJ61IsRyELHEw7YiTUk85bdkyJbB7YQ7LttlGJjsPURiTG0LoZLNFqjDcFUHiwfMUhWIB09k01MT02A8ZCw1bPrlQMCVbUDYURAGaqiGTVuF6w4mkXm+g0+1gy+Y52BEnCWZSTSI/+YpMhjoQ2JaFQrGImZkZTCXkFaQUJIQahg7XdaGqMd+5e7zLxLByGgWYISzHITM9DVmkcEe4jAcgAHZc4ECePBomRLlcxuHDh5FOp9FsNs9ZTs4wOI6Dffv2YePGjWvamFutFt797nfj0UcfxYMPPgiAxUyfOnUKN9988zld6xsQ64QThcCgk+f5NSlyCoUCTpw4gZ07d66IsdV1PSQfjuOQzWaRy+VGNjABoNNxsFiwcCbfxVLBZPEFPlyXZaJks0lI8vhmrOQHn0VBErkVKaEAi50ul8swDAOayoPwMWjqcNEBMLycNghCmKHmsI9aIB/PZDKYnk6ga3qQJR6SxIMX/TJcTyxBTB7dlwlikjudNjqdLgDiD5tqEEUBFEC1UoXrur5AgI8eQJUJzCixgO98Pfi9M00TpWIRudlZSJIEWcLYnovnefDsNhptE5ZpQlaUoS4ThFDwA+VCGsSFSxKm0sykVZERGTiXUCgu27h6Z+jA1j9w6ujNyemN3M5ms2d98jlbsmk2m3j3u9+N3/zN38R73/ves1rLOoZinXDGgVKKhx56CM8//zxuuukm7NmzBzfeeOPYOn7vz544cQK1Wg07duyITA3sdpmlfbFY9De6bFj/HgXPoyhXLSzmTRw/1cThI2eQzmSQSccjs280Ndr0U5H4PkILnxtYOcZzXWRzWQgCB11npatOpwtJFEOng+BEqKo8OhOU04aJBUzTRLFYQi6XRSwmg5LRJwlB4CDLPGIxHhQ8KOFGZgQFJOG4LgzdgG7ocB0XFBSSJCGXzYLnubEniACT9G96xQIBOp0OKpUK5mZnIYhi6BpAI4QAMQmwXMISQrtd6D0RC8Frrypcn0Tbo2xYVY3FQikyIWwGKeoLe+GMi1xqdV/rYrGIEydOYPfu3SNPMkHWTKlUQrfbRSaTYae8qalVVRMCH7YLLrggNNddDQKy+cAHPoAHHnhg1T+/jomwTjiTwDRN/Md//AeeeuopPPPMM7j++uuxZ88e3HzzzUNPI0FKoSAI2L59+6rLcLZth+TT7XZDufWouYdqtYojR45g2yVXoKWLWCqaWCyY6I4RFkgSByuqnKbyMIz+x3jBHbIoIp3JICbzfW7OFHRZdGB0wHMcNE1FMhkHIeN7ILEYj+6AZDpQ2c3OzkIURWZEGnFS4vn+DZsQZlQqihx4gQMhPCg4SDLfd8rzKEU+n2enWTAvsVRCgqSkEIuNNhllcQXR3yVZIn0nCV3XUa/XMTc7G0rjmelnRPmOo+DIcOGBbVls3kfXIfIuMxnVNAg8j3ygIOyRIssi4ESQGwGwa4sDcRVmzfl8HqdPn8bu3bsnjmgOxDalUgmNRgPxeBzZbBbT09Njf8e5IJt77rkHH/rQh3D//fev+ucnwT//8z/jiSeewKFDh/Dss8/iuuuuC//tq1/9Kv7mb/4GPM/jz//8z3HLLbeclzX8AmCdcFYLx3Hwk5/8BE899RR+8IMf4LLLLsOdd96Jd7zjHUgkElhcXMRzzz2H3bt3D5VirhZB1nqxWESr1VqRNri4uIiFhQXs2rVrRcO+VrexVDSxVDBRKFvLIW0T9G5AfduYHucA13WRLxSQSCTCTUvThLEDqLZtw3UN1GoGKOjIjBk2J9Jf/mm1Wmg2W5ibmw0b9oyUookyKmxOFDjflYGHILKTwlI+j9RUBvEEkyJTSuG5JhqtDjqdDiRJ9EUHKjv5+JhELMBzYCcz/zvXarXQarUwNzsLrkeMIIvR5a3gdDMOHKHwqAddN6C32+h2u8zMdGqKWe2Ea4++Xkql2D4/eTltcXERS0tL2LVr10TVgGGglKLVaqFUKqFSqYQR0Nlstq80bds2nn/++bGmn+PQaDRwzz334MMf/vB5IxuARZlwHIcPfOAD+OM//uOQcF566SXcf//9ePbZZ7G4uIi3v/3tOHr06DmPYvgFwTrhnA08z8PPfvYzPPnkk/je976HZDKJU6dO4fHHH8e99957Xq5Xq9VQLBZRr9cBMBHD1VdfHdl8dV2KUsXCYsFEtW4jX7RAx7xNMbl/Yw/dnjPpZUkrAXiBgxexFwXlNNd1/btvJjpQVX/gUZb7SIJS2u8d5p8QeY5gEo1UTOEnKil2zN7nVggl3RwHSBIPWSLgBAGEI6CUQ9eyoOsddDqG70GnMdnyBEFrMRkw/ZNLo15Hp8OiDHp7LgJH4Q3xpxuEIkWThCIy00/HZSmdU1NTIIQwp4ZQsRdDIq71rWEYLsq5mElM9pU+ffo0SqUSdu3adU43zaDkXCqVYNs2MpkM0uk0Xn31VVx88cUrIkImQUA2H/nIR14zBdrNN9/cRzhf/epXAQCf+9znAAC33HILnnjiCfzKr/zKa7Ke1xjrXmpnA47jcN111+G6667Dr/3ar+G3f/u3sXfvXnz961/H3/3d3+GOO+7A3r17MT8/f06M/oJsl6mpKRw8eBCEEMiyjJ/97GeIxWLI5XKYmZkZWn7geYK5nIy5HDsFmZaHQslEvmQhX7TQaPXfonP88nq73S5K5bJvU79MbIo8Ov0zACFA13T9NfBI+qcjzzeLbDaaMC0TU6kYBJGFhFUqVQCUbcg9r5siExgRLgU8z0WSDRBEGrDyX6HQ7x7geUC364IjHDrtZZdRQoCYJCOpxuBRB51OB6V8BeAExLQ4NC0OSZKGfqtcj7lDVGs1OLaN2bm5FZ8JQUTkSUngaSTZAL4wwnFQyOd9M1N2KtBUlSn2TBNWt4kziw0IvBCKJgadGjiCiVM9T548iVqtht27d69JzTkOiqJg8+bN2Lx5MxzHQbFYxIEDB0LVJ6UU09PTE5NcvV7HPffcg4997GPn5eZwUpw5cwY33HBD+OdNmzbhzJkzP7f1/KJgnXDG4PDhw/ijP/oj/OhHP0I2mwWlFCdPnsTTTz+NRx99FKZp4vbbb8eePXvWlCzYC8uy8MILL2B2djYs2QXKn2KxiOeffx6CIITlh1GKN1nicMHGGC7YyDaiTtdFvmghXzJRKJmhNFnXddTqdczNzUEcKI+wTWX8mUNRuKG9JI4QxDUNcU0D4YBux0SrraNQKEAQRKTTU+HMU4AIRTW7nkyiy2kiB8um/l1zeaR7wGBUAaWAZXk9nnIxZGfi0A0XnbaBZmUBrmsjkdSQSCQR01QQwvnGoATlchkghJV+hlofRX8uRGG4rLoXPKEwurZPpFkoA6VWpkyTkUpkkfZYtLahGygUC2zWKkyVlTAV98BPwB3Hjx9Hq9XCzp07zznZDMJ1XZw+fRo7duxAJpMJ3Q6OHTs2kV1NQDYf//jH8e53v/ucrWucRc2dd9459GeGVY7W83XWS2qRcF136N1VIEP99re/jW9961soFAp4xzvegTvvvBM7duxY1ZdT13W8+OKL2LZt29jckE6nE4oOeg0LVyM71Q0X+188iWMna9ASG6Eb/W8pIQDHc9G2MbHhhNMLVeXR1p3QFkeW5WXRAc/7ogMNhIu+71EUHlZkOU1AudpGrVbH3NzscBeGCeIKADYf1OvWECZs6kZoMjqTVtFo6VBVGbncDHie8zNyCChhMnBRIJGzMAAzB40KWiNeF2fyZcyOsDMCmESbOR70w3OZQ7du6LAtGxfOdLFlQ3KkaoxSildffRXdbhdXXHHFeScb0zSxb98+XHLJJUPjDAzDCFVvgV1NNpsNQ9rq9TruvvtufPKTn8Q999xzXtc6DOsltQkfuE445wb1eh3/9m//hm9961s4cuQIbr75ZuzduxdvetObxpYDarUaDh8+vGrDQ8uyQvIxTRMzMzPI5XJjUxIppTh69Chs2w43EaPjoli2UCxbKJQt2DaNNOFkew8Z6bYdgOcpTp1eGmqLY/vZPq6jw7SZ4k3TtKFlQ+b4HP2ZNk0d1Vq7T4wwCFXlIk9KskjGJ3ZS34WhVoLrsdiIoO/Te1122uPggYDnCTiOgBAWYUBDNRoHkY/u8XS7XTRqRWRz82OVXYo0QdooodicKKBcLqFer4eqsZmZmTBb6ejRo3BdF5dffvl5vzNfbXaObduoVCoolUr44he/CFVVcfz4cXz605/Ge97znvO61lEYJJyDBw/iPe95TygaeNvb3oaXX355XTSwTjjnHp1OB9///vfx1FNP4bnnnsMNN9yAvXv34qabbuq7Mz1z5gzOnDmDnTt3jh0KjYLjOKHird1uhwajQUMZYCe1AwcODPV761t710W5aqNUtVGq2KjW7RWnHVXl0ImIUHAcC4ViCTMzo8t/ADu56IbtOx0sT9trmgZJkkFItDqNAtDbdeiGjdnZ0ZY/AJONR0VSM+HB6Md4rodyaQnxZBrxeJyVrnynBmC5dCWKImSJGys84DgCTWWDrRznkxKHMIyNgsDodFCrlTE/P97zDfCzfSIIJ5vwsCW37CMYqMbK5TIEQYDneYjFYrjyyitfM7K59NJL12TPn8/n8cgjjyAej2NhYQEXX3wx3ve+940sdZ1rPP300/joRz+KUqmEqakp7N69G9/73vcAsJLbN77xDQiCgD/7sz/DO9/5ztdkTT8HrBPOLwps28aPf/xjPPnkk/jxj3+MHTt2YM+ePfjhD38ITdPw5S9/+Zze9XieFxqMNhoNJJNJZDIZnD59Ghs3bsTGjRtX9ftcl6JSs1Gs2CER8TzGltOMTgd6u4J0ZvzduCCsLCN5nheadFp+OFsmHQcvDJ+XCYZVJZEiNZUbu0GyYLfo5zxYTuuF6zB12IYNGfDCylJmr8kogQU5Nt5kFGDxD86I6+m6gXq9hm0XbQDhBHA8IymOMGLqzcvhCAXh+cjZoUs3uEjGVl6PUooXXnghtHtyHCd0Cxh3cl4rzjaorVqt4u6778ZnPvMZ/MZv/AYopTh8+DDy+Tze8pa3nNO1rmMs1gnnFxGe5+EnP/kJPvjBDwIAtm3bhjvuuAO33XbbeQlfov4E+uHDh1miYzIZKt7OZo6i2XJQrjkoV22UazaaLTcsr7XabTSbTWy5cAOcEWaWATSVH55u2nMt1+mi2eqi0+1AlmSogcsyYSW9YqkEQRAwP5eNlDCrsckye0apxQIJ+fT0NFJJNfp6CkG1wchnlMmoJJGRJ5J2i72Wc3NziMWECSTaTHjAcWw+iONYWY/z/z9IU911EV2hbQhimuPxOC666CIQQvpKV+12G1NTU2FGztn2dAKyWWtQW0A2v/M7v4Nf//VfP6u1rOOssU44v4io1Wq46667cNddd+GDH/wgDh48iCeffBLf+c53kEqlcMcdd2DPnj0rZMNrRb1ex6FDh3DVVVchHo+j3W6HHm+iKIYGo+OcoCeBbXso12wcPLSAM0stJKbmYVrRG5KscBMIAVg5LZD8Gr7LMs/zcBwHWlzD3Oz0REIAUeofeB15vSGkZJks7C6byyKZUMZ6ogWQJC5UxI0yGZ2Z1mAPMRltNlvQ223Mzs1Clkbb+PQiqnwHAJtzBJduXnmqfPHFF5FKpUbGNAfu6EFGjqZpYd9nUseBAEEq6BVXXDE2F2gUXguyGeUgcOLECVx++eW49NJLAQA33HAD/vIv//K8rOGXCOuE84uITqeDn/70p7jpppv6/p5SimPHjuGpp57Cv/zLv4BSGsqtg7vN1SIwF921a9fQHophGCgWWcIjAORyOeRyuRVGpJOAUoojR46ETWaO49DWXVTqNqp1B5W6g1rd6SsbiWJ0JDXArGsGTUaDWG1RFOG4DmIygSAloGnqyM1PkiaLpJakleWtbreLcrmC2VyOhdjFxvd4gPGbPzMZZVY1tmXAAx86NYiigHq9gW63i9lcDoQj0BQO3Yg5HpEn8Cb43l93KcFUvEeS7idnTk9P44ILLoj8eaBfrt9rUJvNZiPzcHRdxwsvvLDmVNBKpYK7774bn/vc5/Cud71r1T8/KUY5CLwOwtLOB9YJ55cV1Pf9+ta3voWnn34atVoNt956K/bu3Rtu5lE4efIkyuUydu7cOdHdp2maoeLNtu1Q8TYqUrsXgRghHo/j4osvHquQa7RcVOsOqnUbuuGhWHXGBtLJIrei58KGHgvITGeg+uTI80CjqfuiA89v2qtsWNNfzyTqNEXiYA1czzAM1Ko1zAYya8pOSoOzPIPQYsMNS3sRlNNchzk16LoOyzTB+XYviiwDZLKTiyoTmBGnLlkEfnUH6ROS7Nu3D3Nzc6vu7fWCETKTLJumGUqWB1NxzxXZfP7zn8fevXvXvN7VYFB9tk44Q7FOOK8X1Go1/Ou//iuefvppHD9+HG9961uxd+9eXHvttSvEBsNkz6vFYMBWYDA6uHkEj92/fz/m5uYmSl8chOdRNNsuag0H1YaLWtNBvbF8EoqrPIwekjAtv6zVM/Qoy1xfeYuJDphijIkOFKgqm/dxI2aLBstp7baOZqOB2R6ZNXOPnqScxkdnBMV6Ti4UKFcq8DxGmIZhwDJNxDUZMS051mQUmIyULsgRbPfLaWdr+T8KgUdgqVQKU3GDXKiXXnppzRHU5XIZd999N77whS+8ZmQDDCecK6+8Etu3b0cymcRXvvIV/K//9b9es/X8gmKdcF6P0HUd3/3ud/H0009j3759ePOb34w777wTb37zm9HtdvH1r38d73rXu8aeNFaDUZHamUwGlmVh//79a/a7GgVKKVq6h1rDYWTUdP2TkYFKuYLcbK7PIFRThZHlrWBY07Z0tA0LkiSH0c7DXh+pZ9NuNprQDWOFzHqScpoirTyZrVibfz3XY38olUrgeB7TmUz49aWUgtAuao2ubzIq+emg/SajghAdewAA119KkIqTs3ZhnhSBd96ZM2dQKBSQSqUwPz8/NphwGAKyefzxx7Fnz55ztr5JHAQGCcc0TbTbbUxPT+O5557Du971Lhw8eHBNvajXEdYJ5/UOy7Lwgx/8AE899RR+9KMfwbIsvPOd78SXv/zlNfVhohA0jYvFIiqVCizLwoUXXogLLrhgzYq3SVEsFnH05eO44KIr0TEFNFqu/58DXuAjy1tBOc00zdDpYDlfJgae55fLaRSo1euwTBO52X6ZNQEgiNEnl0nKabJIYFNfaVcsQZIkpKemVnx1JZGRErPfsULRASEEmqZB0zQk4wJMO8L0UwJ+dQcHy7Kwb98+XHTRRef0RmEUWq0WDhw4gJ07dwJAaNQJoK/vM+oGqVQq4e6778YXv/hF3HHHHed9vYMYJJzV/vsbBOvmna93SJKEW265BRdddBF++tOf4rHHHsOZM2fw1re+NZRb33rrrWuSnA4Dx3HhFHitVsMVV1yBVquF//mf/5koUnutWFhYQD6fx5v+n2tW9KM8z0PboGi2PTTbLhptD622i5bhLUdQUwrbL1vJsgxZlpHJLDsdFAoFAAQz0xp4UUOz0YTneezOf+BrpEgEZoTKjQATiRN4gcAymWw9pqpIpVbeIUsiCcuALPtHgixLANKwbScUflQrHmQl7g/LikM379k0Ce1jtm3bhunp6ehFniWazSYOHjyIXbt2hWICTdOwZcsWWJaFcrmMl19+OQxoy2azfcPKAdk88cQTuP3228/7eidBqVRCJpMBz/M4duwYXn75ZVx88cU/72X90mD9hPNLDEop7r33XnzhC18I7yA9z8P+/fvxSV2MgwAAHzlJREFU5JNP4rvf/S5mZmawZ88e3H777chms2dVasvn8zh16tSKjJ61RGpP8txOnDiBRqOBHTt2rGo41vMomvoy+TR1VqZrGx68ISIF13HQNTuo1hoApUgmk/7mLfWRzkTlNJmLJBwKNvS6uMg85hLJ4Q10VeEi460lgcBymEO3YeiwLBuxWAyaprJ8HP/93rnFxLGX9695on+1aDQaOHToEHbu3BmpXOsNaCuVSvja176Gm266CX//93+Pr3zlK7jtttvO+3oHMcpB4Mknn8Tv/d7vQRAE8DyPL33pS+e0zPdLivWS2jrYpv3yyy+HcmtRFHH77bfjzjvvxKZNm1ZFPidPnkSlUsHOnTvHltDWEqk9bN1HjhyB53m47LLLzplxpOdRGF1GPi3DYySke+haLo6dLEJRFCQTCeaUoOuwfacDTdOgKDJEURirqgMALcahGxHtIPAeFhaLSKVS0OIjjFdpT49nDFSF9JXTgr6V7puMyrKEZFzEtHAUV1xxxTk78Y5DvV7H4cOHsWvX/9/euUdFXeZ//DUwQBAIoqAgKix4FwTF1VNqeKGL4mBZitVCa25tu7Za28U9bv20LRGXyMo9Wbsq2ZZsyU2UKHM1NzclM1EQARGQOwNyEeQ68/39QfNdQNAZbqPwvM7pdBqY+X7GnO97ns/zed7vaQa3dzUaDYcOHeLtt9+mpqYGDw8PVCoVgYGBjBw5so8qFvQQITiC9kiSRGFhIbGxscTFxVFbW8tDDz3E0qVLmThxokGGn/piaKQ2/O/Eu5WV1U0933qLlpYWUlJSsB82Ajt7J2qvS9TWt66Gauu0qK/WUVVdh1ZzHaXZ3VhZte77dFaXQgFK5c2dtls0GiorirGxc8DKquubsYVZ1w4E7X/PhJYurqc7L6Opu4yT3XUsLS3lLwA9PezbFT0RG2g9P/boo4/y1ltv8eCDD3L58mUSEhIYP378QPYiu9MRgmMoSUlJrFu3Do1Gw5o1a9iwYYOxS+pTysvLOXDgALGxsRQUFLBo0SJUKhU+Pj6yqDQ3N5Oent4rN/9bRWpD683/3LlzDB8+XO9DiD1Bt4E+duzYm05rNTZJ1F7XUFZ+jeLSKtQVtUiKu1BaDEFpdjeKn402Le9S0HSTzXtdcNrIkY6Y36LdqG87TXOT6bTGn90RHrrXnpEO1ly/fl1uW0mSJJ+3MiTe4mZUVlaSkZGBt7d3t9qpHcVGcMcgBMcQNBoN48eP5/Dhw7i4uDBz5kz27dvH5MmTjV1av3Dt2jUSExOJiYnhwoULzJ07lwULFrB161beeOMN/Pz8evV6HSO1bWxsZIPRsWPH9kvrROflNW7cOIM30HUrB7VaTWmZGo3WjLtthnO3tT0aLKhvlOR/Ghpbf7/p57hrF2cHTM1v8c2/m+20tjQ2NlJWpsZtjCN+02+8+es27dVqNfX19bLDeGfnrfTh6tWrZGZm9lhstmzZwgMPPGDw8wVGRQiOIXz//fds2rRJthXvGJ40mGhsbCQqKopXXnkFNzc3Jk6ciEqlws/Pr0dDAF0hSRJqtZr09HRMTU2xsbGR2z6GenTpi+7Ee2/taXTct9I5LFtbWyMB6vJrnEvNxNVtAkpzS643KmhskmhogoYmicbm9gmRd90qj+dndCPTndVTXl7OiBEjGT/aDPdRt3aLaHveSmfyqpvGuhUVFRVcunQJb2/vbrXqSkpKeOyxxwgNDeX+++83+Pn68vLLL5OQkIC5uTnu7u7s2bNHdqkODQ1l165dmJqa8t577wnRMwwxFm0IhYWFcqwztOaPnzp1yogVGY/s7GzeeecdYmJimDVrFt999x0xMTH83//9HxMnTiQwMBB/f/9uWZN0Rm1tLdnZ2fj4+GBjY2NwpLahVFdX9+jEe2fcddddjB49mtGjR8tODTk5OVy/fh0rKytqamq455c+XbautJJEYxM0NreuiJpbJOqbFDQ1tz7W+m9oavmfMJkrFZ2KTX19PRUVFYwcORKlUomjHgNppj9b6ehi1KurqykrKyM7O5u77rpLdhjvbOS9vLxc/v/XnZF4ndhs3boVf39/g59vCP7+/oSGhqJUKnn11VcJDQ0lLCyMCxcuEBUVRVpaGkVFRSxatIjMzMyBGpZmVITgIPLH22JhYcG+ffuYNGkS0Hqwzc/PD61Wy5kzZ4iOjiYiIgInJyd53Lq7Zzp0bRgvLy/5ZmxtbS37sukitVNTU7sdqd3Z9by9vfvkcCyAmZkZTk5OODk5oVarycjIwNbWlnPnznW5cjBRKLC0aI0X4CYaKEkSTS3Q1NwqSk0tCppaoPlnMaqorOHqNTW/cB2DhBJzM7CxMuzvsUKhwM7OTv7mr/sCkJKSgkKhaHdYU61Wk5OT02OxCQsLY9GiRQY/31Darp5mz57N/v37AYiPjycoKAgLCwvc3Nzw8PAgOTl5oMZBGxUhOLSuaPLz8+X/LigowNnZ2YgVGQ93d/dOHzcxMcHX1xdfX1+2bNlCeno6MTExrFixAktLSwICAlCpVDg5Oekl1qWlpeTl5eHj49NlG8bS0pIxY8YwZswYOVI7MzNT70jttpSVlZGbm3vT6/Umuuv98pe/xNzc/IaVg6Wlpbxy0Ld1qFAosDBrNeHs2MUoKyvjWmkuyxZ69+rh27vvvhs3Nzfc3Nxkk9eMjAzq6urQarVMnjy5W63P4uJiHnvsMf7617+ycOHCXqtXX3bv3s3KlSuB1g7H7Nmz5Z+5uLhQWFjY7zUNBoTgADNnziQrK4ucnBxGjRpFVFQUn332WY9e09XVFRsbG0xNTVEqlZw+fbqXqjU+CoWCyZMnM3nyZDZu3EheXh6xsbGsWbOGxsZGOVrBw8OjUzEoKCigtLQUHx8fvW9W5ubmcmKpLlI7Ly9PjtTWTbx1dr3CwkKKi4sNul5PKC4uprCwsN312q4c2tr7//TTT5iamspODd3dcL9y5Uqfvz8LCwtcXFwwNzcnJyeH0aNHU1JSQlZWlkHhbH0pNvr4o7311lsolUqeeOIJQHQ4+hMxNPAziYmJrF+/Ho1Gw+rVq9m4cWOPXs/V1ZXTp08zfPjwXqrw9kc3ABAXF0dcXBylpaX4+/sTGBiIp6cnAPv27WPq1KlMnTq1V3rknUVqt21b5ebmUllZiZeXV7/05PPz81Gr1UybNk3v6+lah2q1Wh460I0r3+rGV1RURFFREd7e3n3uaQf/Ezdvb29Z3AwJZ9OJTXh4OAsWLOjzejvy8ccfs3PnTo4cOSI7IHQcEnrggQfYtGmTaKnpj5hSMzaDUXA6Ul1dzaFDh4iNjeXixYvY2Nhga2tLVFRUn3wTb9u2qvjZ6t/c3Jxp06b1usdbZ+Tm5lJVVWWwFU9bdIdl9RlXLigooKyszCBx6wklJSXk5+fj4+PTpbhJkiQny1ZUVGBqakpTU5Mc7rdixQrefvtt5s+f3+f1diQpKYkXX3yRb7/9tp1xaVpaGo8//jjJyckUFRWxcOFCsrKyxNCA/gjBMTZubm5yi+fZZ5/lmWeeMXZJRqOxsZFVq1Zhbm6Oubk5Z86cYfbs2ahUKubNm9frYiBJEhcuXECj0WBlZUVFRUWvRmp3dr3s7Gzq6+uZMmVKr1nxdBYP4eDgwLBhwygoKJCthvrjxqhrExq6kmpoaCAhIYH33nuPgoICFi9ezPr16/Hy8ur3tpWHh4ccEAft46Hfeustdu/ejVKpZPv27cLVwDCE4BiboqIinJ2dKSsrw9/fn/fff/+GaOnBwu9+9zs8PT157rnngNZv8cePHyc6Oprjx4/j6emJSqVi0aJFPT71rrPGufvuu9vlAvVmpHZbdL5vkiTd1CKop+iyZcrKyigpKUGhUODh4dGn55V0FBUVUVxcjLe3d7fErbCwkBUrVvCXv/yFmpoa4uPjyczM5MSJE7c09hTcEQjBuZ3YtGkT1tbWvPTSS8YuxSg0NTV1uYrRarUkJycTHR3N4cOHGTt2LAEBASxevNhgV2ONRkNKSsotrXF6Eqndsfb09HTMzc27HJDoTSRJ4vLly9TV1TF27FjKy8upqKjok/NKOgoLCykpKem22BQUFLBy5Uq2b9/OfffdJz/e0tLSL3tOgn5BCI4x0Y2M6g4y+vv78/rrrwt/qFug1WpJS0sjOjqaxMREbG1tCQgIYOnSpYwYMeKmN3RdiqWLi4tBkcmGRGp3rPX8+fMMGTIEV1fXfhGbrKwsWlpamDRpUrvrdRw60MVD9HS12NM9Ip3YvPvuu4N2dT9IEIJjTC5fvszDDz8MtH6Te/zxx7s19bZ69WoOHjyIo6MjqampQOvhxZUrV5Kbm4urqyuff/55v+Sb9De6b/O6aAVJkuRxazc3t3Y33IaGhl6Ju75ZpHbbfRmNRsO5c+cYNmxYv5iM6tp2ABMmTLipuOk80to6dDs4OBjskZafn095eXm394jy8/NZuXIl77//PnPnzjX4+frQlVVNbm4ukyZNYsKECUD7vRpBnyAEZyBw/PhxrK2tCQ4OlgXnlVdewd7eng0bNrB161YqKysJCwszcqV9iyRJlJSUEBcXR2xsLJWVlTz44IOoVCq0Wi3bt28nPDy8V4W3baR2ZWUl1tbWcrRCWloazs7O/XI4WDcAYWZmxrhx4wwSDZ1Dt1qtvqmAduTKlStcvXoVLy+vbg1A6MRmx44dzJkzx+Dn68vXX3/NggULZKsagLCwMHJzcwkICJA/M4I+RwjOQKHjh2fChAkcO3YMJycniouL8fPzk7/9DhYqKytJSEggMjKSc+fO8fDDD/P444/j6+vbJxNbkiRx7do1eVLLysqK0aNH90mkdlt0LUYrK6t2AxDdfa2OZ2V0Tgdt91Ly8vLk0e7uiM2VK1cICgrib3/7G/fee2+36zWU2NhY9u/fz6effioEp/8R5p0DldLSUnmPwsnJibKyMiNX1P8MHToUd3d3KisrOXLkCNnZ2ezatYvnn3+ee++9F5VKxZw5c3ptekuhUGBubk5VVRVeXl5YWlrK/mK6SG0HB4de9Wdru0fk5ubW49czMTHB3t4ee3v7dmdl8vLy5JHxhoYG6urqui02eXl5rFq1qt/FBtpb1QCyx9uQIUN48803+6ytJzAMscK5zen4bc3Ozo6qqir550OHDqWystJY5RmNP//5zzz33HOMGjVKfqypqYmjR48SExPDiRMn8PHxYenSpSxcuLBHYqDLzpkwYcINbbvOogl0E2/dpb/3iOrr67l48SLV1dVYWVnJ55UMGTrIy8sjKCiIDz74gHvuuafXatPXqub06dPExMSgUChobGyktraWYcOG8eOPP7Js2TLS0tIYMmRIr9UlaIdoqQ0UREute2g0Gv773/8SGxvLkSNH8PDwICAggAcffNCgDBxDsnO6E6ndWd0pKSk4Ojri4uKid509ITs7m+vXrzNlyhRaWlrkiTd930Nubi6rVq3iww8/bGeC2R90ZlXTET8/P8LDw/H19e3X2gYRQnAGCh0F5+WXX2bYsGHy0MDVq1fZtm2bkau8vdFqtaSkpBATE0NSUhLDhg2ToxUcHBy6vJHW1NSQlpbWrewcfSK1O9LS0sLZs2f7dSAhOzubhoYGpkyZcsOfQ8f3YGdnh6OjY7v3YEyx6cqqRq1Wy156ly9fZu7cuZw/fx57e/t+rW8QIQRnILBq1SqOHTv2c3rjCDZv3syyZctYsWIFV65cYcyYMXzxxRd6f5A6G7PetGkTf//73+UP7JYtW1i8eHGfvSdjozvPEhMTQ0JCAkqlkiVLlhAYGIiLi4t80y0rK+Py5ct4eXn1+DR8Z5Hajo6ODBs2TB5y0J0jGjNmDCNGjOjx+7wVkiRx6dIlmpqamDx58i1XYG2n9nJycvjoo4+47777+Oyzz9i1axezZs3q85o70pVVTXR0NK+//jpKpRJTU1M2b97M0qVL+72+QYQQHMGNdDZmPZhdECRJorCwkNjYWOLi4qitreWhhx7Czs6Offv2kZiY2OtBbZIkUVNTI5tbWlpaYm9vT1FREW5ubjg6Ovbq9bqqoatDpPqg1WqJj48nPDycpqYm3NzcWLZsGcuWLRvUZrWDGL3/AvWOy6DgjmDevHmirdAGhUKBi4sLzz//PEeOHOHQoUOUl5cTGhqKJEls3bqVH3/8Ea22kyznHlzT1taWcePGMWvWLEaPHk1OTg4tLS3k5+eTn59PQ0NDr12vI5IkkZmZiUaj6ZbYQGsbbdu2bXz00UekpaWxfft2qqurSUlJ6YOKBQMJMRYtYMeOHezduxdfX1/efvvtAelcoA9JSUmkpqaSkZGBqakpiYmJ7NixgwsXLjB37lxUKhX33HNPr3mANTY2kpmZydSpU7G3t+/1SO2OtHUs6K7RaHZ2Nk8++ST/+Mc/mDlzJtDa2vrjH//YKzUKBjaipTbI6DiEUFpayvDhw1EoFLz22msUFxeze/duI1dpHL766ivmzJlzww2+sbGRb775htjYWE6ePImvry8qlQo/P79um2XqRq0nTpyInZ3dDT/XRWqXlZV1K1K7I5IkcfHiRUxMTBg/fny3XuPSpUs8+eST7N69u88mvl577TXi4+MxMTHB0dGRyMhInJ2dkSSJdevWkZiYiJWVFZGRkUyfPr1PahAYjNjDEXTOzU5hixPat6alpYXvvvuOmJgYjh49ysSJEwkMDMTf3x8bGxu9XkM3aj1lyhS9zoboIrXLysr0itTuiCRJpKenY2Zm1m1X66ysLH71q1+xZ88eZsyYYfDz9aWmpkb+M3nvvfe4cOECO3fuJDExkffff5/ExEROnTrFunXrOHXqVJ/VITAI4TQg0I/i4mLZuSA2NpapU6ca9Pz8/HyCg4MpKSnBxMSEZ555hnXr1g1Yk1GlUomfnx9+fn5otVrOnDlDdHQ0ERERODk5yePWusmpjtTW1nL+/HmmTp2qt0AplUpGjBjBiBEj5EjtkpISMjIybojU7ojOi83CwgJ3d/dui01wcHC/rCraCnBdXZ1cb3x8PMHBwSgUCmbPnk1VVVW7v7uCOwOxwhlEdDZmfezYMc6ePYtCocDV1ZUPP/zQoA9xcXExxcXFTJ8+nWvXrjFjxgzi4uKIjIwcVCajulVETEwMhw4dwtLSkiVLlqBSqXB2dkahUJCamkp1dTXe3t69si/TNpRN54+m2/dRKpVIkkRaWhqWlpbd9mLLzMwkJCSEPXv29FsLa+PGjezduxdbW1uOHj2Kg4MDAQEBbNiwQTYDXbhwIWFhYeIw5+2BaKkJjENgYCBr165l7dq1g9YRQZIk8vLyiI2NJT4+nsbGRmbMmMGXX37JgQMHesUbrbNr6vzRysvLMTMzo7m5maFDhzJ+/PhuvaZObCIjI/Hx8em1WvWxqwEIDQ2loaGBzZs3s2TJEv70pz+1E5xt27b1aXtPoDdCcAT9T25uLvPmzSM1NZUxY8YIzzdaheDAgQP84Q9/YMqUKZSWluLv709gYGC3TTJvhVar5ezZs0CrWwAYHqmdkZFBSEgIe/fuxdvbu9dr1Ie8vDyWLFlCamoqzz77LH5+fqxatQpob/EkMDpiD0fQv9TW1rJ8+XK2b98uTBLbcPLkSd58801OnjyJk5MT1dXVHDp0iIiICDIyMvDz80OlUjFr1qxeiVbQuUzb29vj6uoK/C9SOz09Xa9I7YsXL/LUU08ZRWyysrIYN24cAAcOHGDixIkAqFQqduzYQVBQEKdOncLW1laIzR2IWOEIekxzczMBAQE88MADvPjii4AwGdVRXV1NU1NTp0mk9fX1HD58mOjoaH788Udmz56NSqVi3rx53crZ0Wq1nDt3jqFDhzJ27NhOf6erSO0hQ4ZgYmIii80nn3zCtGnTDK6hpyxfvpyMjAxMTEwYO3YsO3fuZNSoUUiSxNq1a0lKSsLKyoo9e/aI/ZvbB9FSE/QPkiQREhKCvb0927dvlx8XJqOG0dzczPHjx4mOjuY///kPU6dORaVSsWjRIr0GDLoTaaCL1C4uLmb16tX84he/4OLFi/zrX/8SeyMCQxCCI+gfvvvuO+bOndtuP2LLli3MmjWrWyajXY1ZDyaTUa1WS3JyMtHR0Rw+fJixY8cSEBDA4sWLOx0t14nN8OHDGT16dLeumZKSwosvvoi7u7s8tr1mzRrmz5/f07cjGPgIwRHcmXQ1Zv35558PSpNRXcy0btza1taWgIAAli5dyogRI6itrSU6OppFixZ1Oz/nwoULrF69mk8//RRPT08kSeKnn36irq5OJGUK9EEMDQjuTJycnOTNYBsbGyZNmkRhYaGRqzIeJiYmeHp64unpyeuvv87ly5eJjY0lJCSElpYWrl27RmBgYLvkU0PQic1nn30mH/pVKBTCNkbQJwi3aMFtS25uLj/99JOctbJjxw68vLxYvXr1oByxVigUuLu789JLL5GYmIhSqWTmzJn88MMP+Pn5sWXLFtLS0vR2t05LS7tBbPqC1157DS8vL7y9vbn//vspKioC4NixY9ja2uLt7Y23tzdvvPFGn9UguD0QLTXBbUltbS333XcfGzdu5JFHHhEmox0IDAwkKChIPpdSWVlJQkICsbGx5OTksGDBApYuXYqvr2+n49ZpaWk8/fTT7Nu3jylTpvRprV35ox07dozw8HAOHjzYp9cX9DmipSa4c2lubmb58uU88cQTPPLIIwDtUjB/85vfEBAQYKzybgs+/vjjdi7TQ4cOJTg4mODgYK5fv05SUhK7du3i+eef595770WlUjFnzhzMzMxITU1lzZo1REVFMXny5D6vtSt/NMHgQ6xwBLcVXY1ZtzVqfOeddzh16hRRUVHGKvOOoampiaNHjxITE8OJEydwdXUlMzOTuLi4fhEbHZ35ox07dozly5fj4uKCs7Mz4eHhfb7aEvQJYkpNcGfS1Zj1vn37emQy2tDQwLx582hsbKSlpYVHH32UzZs3k5OTQ1BQEFevXmX69Ol88skn3Tp0eSeg0Wj44osvsLW15aGHHurV1+6OP1pNTQ0mJiZYW1uTmJjIunXryMrK6tW6BP2CEByBoC2SJFFXV4e1tTXNzc3MmTOHd999l4iICB555BGCgoL47W9/y7Rp03juueeMXe6Apa0/WkdcXV05ffo0w4cPN0Jlgh6gt+CIKTXBoEChUGBtbQ207hE1NzejUCj497//zaOPPgpASEgIcXFxxixzQNJ21dLWH62kpATdF97k5GS0Wm2XOUKCgYEYGhAMGjQaDTNmzODSpUv8/ve/x93dHTs7O5TK1o+Bi4vLoD7z01ds2LDhBn80gP379/PBBx+gVCqxtLQkKipKDBQMcITgCAYNpqamnD17lqqqKh5++GHS09Nv+B1xw+t9oqOjO31cl5skGDyIlppg0GFnZ4efnx8nT56kqqqKlpYWAAoKCnB2djZydQLBwEUIjmBQoFar5UC4+vp6vvnmGyZNmsT8+fPZv38/0Hq2pe1ElUAg6F3ElJpgUHDu3DlCQkLQaDRotVpWrFghe5PpxqJ9fHz45z//iYWFhV6v2dWo9VNPPcW3336Lra0tAJGRkUZLzRQI+gExFi0Q9DVdjVrv3LmTgIAAefptoBIeHs7LL7+MWq1m+PDhSJLEunXrSExMxMrKisjISGECOjgQY9ECQV/T1aj1YCA/P5/Dhw+3C3v78ssvycrKIisri48++kicZxLcgBAcgaAHaDQavL29cXR0xN/fX3a23rhxI15eXrzwwgs0NjYaucre54UXXmDbtm3tBDY+Pp7g4GAUCgWzZ8+mqqqK4uJiI1YpuN0QgiMQ9ADdqHVBQQHJycmkpqYSGhrKxYsX+eGHH7h69SphYWHGLrNXOXDgAKNGjWLatGntHi8sLGyXOCrONQk6Is7hCAS9gG7UOikpSU4ltbCw4Ne//jXh4eFGrs5wbuaNtmXLFr7++usbftbZfvBgaTEK9EMIjkDQTdRqNWZmZtjZ2cmj1q+++qrsbC1JEnFxcX0abtZXfPPNN50+fv78eXJycuTVTUFBAdOnTyc5ORkXFxfy8/Pl3xXnmgQdES01gaCbFBcXM3/+fLy8vJg5cyb+/v4EBATwxBNPyLHQ5eXl/PnPfzb4tTUaDT4+PnLuT05ODrNmzWLcuHGsXLmSpqam3n47euHp6UlZWRm5ubnk5ubi4uLCmTNnGDlyJCqVir179yJJEidPnsTW1tYgR2/BwEeMRQsEtyERERGcPn2ampoaDh48yIoVK25LV+u2Ds+SJLF27VqSkpKwsrJiz549+Pr6GrtEQd8jzuEIBHcqBQUFhISEsHHjRiIiIkhISMDBwYGSkhKUSiXff/89mzZt4quvvjJ2qQIBiHM4AsGdy/r169m2bZscQFdRUSFcrQUDAiE4AsFtxMGDB3F0dGTGjBnyY2L6SzBQEFNqAsFtxIkTJzhw4ACJiYk0NDRQU1PD+vXrZVdrpVIppr8EdyxihSMQ3EaEhoZSUFBAbm4uUVFRLFiwgE8//VS4WgsGBEJwBII7gLCwMCIiIvDw8KCiooKnn37a2CUJBAYjptQEAoFA0BP03lA0dA9H7FQKBAKBoFuIlppAIBAI+gUhOAKBQCDoF4TgCAQCgaBfEIIjEAgEgn5BCI5AIBAI+gUhOAKBQCDoF4TgCAQCgaBfEIIjEAgEgn5BCI5AIBAI+gUhOAKBQCDoF/4ftfVZg3O2Tv8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_trajectories_3d(\n",
    "    trajectory3d(20,0,elevation=ridge),\n",
    "    trajectory3d(20,270,elevation=ridge),\n",
    "    bounds=[0,40,-40,0],\n",
    "    elevation=ridge)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.3 Solving for the range of the projectile in 3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "\n",
    "B = 0.001 #<1>\n",
    "C = 0.005\n",
    "v = 20\n",
    "g = -9.81\n",
    "\n",
    "def velocity_components(v,theta,phi): #<2>\n",
    "    vx = v * cos(theta*pi/180) * cos(phi*pi/180)\n",
    "    vy = v * cos(theta*pi/180) * sin(phi*pi/180)\n",
    "    vz = v * sin(theta*pi/180)\n",
    "    return vx,vy,vz\n",
    "    \n",
    "def landing_distance(theta,phi): #<3>\n",
    "    vx, vy, vz = velocity_components(v, theta, phi)\n",
    "    v_xy = sqrt(vx**2 + vy**2) #<4>\n",
    "    a = (g/2) - B * vx**2 + C * vy**2 #<5>\n",
    "    b = vz\n",
    "    landing_time = -b/a #<6>\n",
    "    landing_distance = v_xy * landing_time #<7>\n",
    "    return landing_distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.4 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mini-project:** When an object like a cannonball moves quickly through the air, it experiences frictional force from the air, called drag, which pushes it in the opposite direction it’s moving.  The drag force depends on a lot of factors, including the size and shape of the cannonball and the density of the air, but for simplicity, let’s assume it works as follows.  If $\\vec{v}$ is the cannonball’s velocity vector at any point, the drag force $\\vec{F}_d$ will be:\n",
    "\n",
    "$$\\vec{F}_d = -\\alpha \\vec{v}$$\n",
    "\n",
    "where $\\alpha$  (the greek letter “alpha”) is a number giving the magnitude of drag felt by a particular object in particular air.  The fact that the drag force is proportional to the velocity means that as an object speeds up, it feels more and more drag.  \n",
    "\n",
    "As a mini-project, figure out how to add a drag parameter to the cannonball simulation, and show that drag causes the cannonball to slow down.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def trajectory3d(theta,phi,speed=20,height=0,dt=0.01,g=-9.81,elevation=flat_ground,drag=0):\n",
    "    vx = speed * cos(pi * theta / 180) * cos(pi * phi / 180)\n",
    "    vy = speed * cos(pi * theta / 180) * sin(pi * phi / 180)\n",
    "    vz = speed * sin(pi * theta / 180)\n",
    "    t,x,y,z = 0, 0, 0, height\n",
    "    ts, xs, ys, zs = [t], [x], [y], [z]\n",
    "    while z >= elevation(x,y):\n",
    "        t += dt\n",
    "        vx -= (drag * vx) * dt\n",
    "        vy -= (drag * vy) * dt\n",
    "        vz += (g - (drag * vz)) * dt\n",
    "        x += vx * dt\n",
    "        y += vy * dt\n",
    "        z += vz * dt\n",
    "        ts.append(t)\n",
    "        xs.append(x)\n",
    "        ys.append(y)\n",
    "        zs.append(z)\n",
    "    return ts, xs, ys, zs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_trajectories_3d(\n",
    "    trajectory3d(20,-20,elevation=ridge),\n",
    "    trajectory3d(20,-20,elevation=ridge,drag=0.1),\n",
    "    bounds=[0,40,-40,0],\n",
    "    elevation=ridge)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4 Optimizing range using gradient ascent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.1 Plotting range versus launch parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scalar_field_heatmap(f,xmin,xmax,ymin,ymax,xsteps=100,ysteps=100):\n",
    "    fig = plt.figure()\n",
    "    fig.set_size_inches(7,7)\n",
    "\n",
    "    fv = np.vectorize(f)\n",
    "\n",
    "    X = np.linspace(xmin, xmax, xsteps)\n",
    "    Y = np.linspace(ymin, ymax, ysteps)\n",
    "    X, Y = np.meshgrid(X, Y)\n",
    "    \n",
    "    # https://stackoverflow.com/a/54088910/1704140\n",
    "    z = fv(X,Y)\n",
    "    \n",
    "#     # x and y are bounds, so z should be the value *inside* those bounds.\n",
    "#     # Therefore, remove the last value from the z array.\n",
    "#     z = z[:-1, :-1]\n",
    "#     z_min, z_max = -z.min(), z.max()\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "\n",
    "    c = ax.pcolormesh(X,Y,z, cmap='plasma')\n",
    "    # set the limits of the plot to the limits of the data\n",
    "    ax.axis([X.min(), X.max(), Y.min(), Y.max()])\n",
    "    fig.colorbar(c, ax=ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 504x504 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scalar_field_heatmap(landing_distance,0,90,0,360)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.2 The gradient of the range function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_scalar_field(f,xmin,xmax,ymin,ymax,xsteps=100,ysteps=100,c=None,cmap=cm.coolwarm,alpha=1,antialiased=False):\n",
    "    fig = plt.gcf()\n",
    "    fig.set_size_inches(7,7)\n",
    "    ax = fig.gca(projection='3d')\n",
    "\n",
    "    fv = np.vectorize(f)\n",
    "    \n",
    "    # Make data.\n",
    "    X = np.linspace(xmin, xmax, xsteps)\n",
    "    Y = np.linspace(ymin, ymax, ysteps)\n",
    "    X, Y = np.meshgrid(X, Y)\n",
    "    Z = fv(X,Y)\n",
    "\n",
    "    # Plot the surface.\n",
    "    surf = ax.plot_surface(X, Y, Z, cmap=cmap,color=c,alpha=alpha,\n",
    "                           linewidth=0, antialiased=antialiased)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qFouBxrWPKkxwRgy3xIBOF38AqFQqOHfuHI4cOYKxsTHf2w07S806BuH48eOIRqNQVdW2TTQaRTQaNQWIXOkuLi6iVCqhWq1iZWUlcMW7H8593/vNv6trdYQmJQBAbbO5MDmtG0Jt07CGrGJD/tfqOqS4iG8ffC/es/itnp6zFdqws2HTi3OyCtCePXtsAmS9MCEuOD8CZHVJDwNyzlsdJjgjhFdiQCeCo6oqLl26hEqlguPHj5vzUPwyTAunVqvh/PnzUBTF9xgE55WuqqqYm5tDtVo1e36RtvvpdLrj6aSAITbVvCEackxsEY52SHHjq+e0hoSwAOsz/fbB90II85ie/2bH5+rGKMZw+nFONAEqFovIZrMtApRKpRCNRlvOQVXVoYozcRNudZjgjADOjgG0D3bQxZ9M4yQLbydXZ93EcLoRnFwuhwsXLuDAgQOYmpoKfHzreQiCgCeffNKseCdzX+7cuQNVVZFMJk1XiyRJvvZLLBs5Znx96uWmaNQ23d1pTjiJgyg19rFRd32cWtIw9/z7ei46oxjDGVRwnljGVgHK5XK4ceMGCoWCLQYUjUZHwqXWi0GHw4YJzpCxJgZ4pTv7FRxd13Hz5k2srKyY0zg3NjYGFvwHOkunJtssLS3h/v37OHHiRNdXdM7X0tp2n4xeXl9fRzabxa1bt6DruulmSSaT1DRYqxutHW7uNBpiQnR9vJgwLhbeee/34cS3vuF7n354HCycdtBcs1YBKhaLqFarCIfDmJycpFpA/YbFcBhdQ2I1fjoG+Fn8K5UKzp8/3zKNc5D1NJ1uV6vVkM/nkUwmMTMzM5CrSUEQkMlkkMlkABjvBxGgpaUlcBxnE6BrH/7XUBKGG66yUe3q2LTkASIs9Q215TYAUCtaT0VnFF1qw7YkALoAvfPOOxAEATdv3kShUEA4HDY/G4MQIGbhMDqmk44B7QTn4cOHuHLlCnUaZ6eWCs/ztpnwfgkqONlsFgsLC5BlGYcPHw58vF4hiiLGxsbMxIparYZcLofV1VWs/uzHoVNeQ6s7TYpKkKJNt5yutj6+eLdCPbYQbn4GxISA+oZqExtCL0VnFAVnFM+JXAzu2rULkiRB13WUSiXkcjlTgEKhkOmCa1cf1gmlUsmzy/ZWgQnOgOm0Y4CbaPiZxjnoFjV+t9N1HdevX8fq6ipOnDiBd999N/Cx+okkSZiYmED2Ez8NOSqjsmm0ovdj3dDEBgAiu4z3p/TQex80sSH0SnRGcXEfBQuHhjVLjeM4RCIRRCIR7Nq1yyZAt27dMgWIWEC9ECBd13va6WBYbP1nsEUgVs2VK1fM1v9BoIlGPp/H/Pw8du7c6TmNs9OOAf0Uqkqlgvn5ecTjcd91QWTfg0aOumezRcaaqda1sv+EgfCEsc/Sw6rNuiFIEWNxqxXp+xQkHhf+1Ut47mv/4PuYTkZRcEbxnADv+iCaAJXLZWSzWdy+fRv5fL7nArRVYYIzAKyJAQ8ePMDBgwcD78MqGrquY3l5Gbdv38bRo0fbDkgbdAynnVA9evQIly5dorr/Ro0rP/bDNuvGSnQigloxuMvRSnhChiALKK01XW1EbMjfVtFRkrJpPalVtSvReVyz1DrFr0hwHIdwOIxwOOwqQIqimC64eDzuue9RfJ86hQlOH6ENSOsWUp8iSRLOnDnjK925mxhOL4VK13UsLi4il8vh1KlTPS/E7DW3f+bHW6wbURFRQbVFbKzWjZs7zYtwRrGJjhWn6HAC3zPRGbUr7VG1cLrBKUAATBfc8vJyiwDFYrEW0d0urwsTnD7hTAxwzsbo5MNTr9cxOzsbuD5lFGI4pLVOOp3G6dOnR/7L8+hTPwW1Rn/NohO9S08V5OYFQzhjxHfqZXtNjhSRIEUk2/lYRQdAR6IziovYKFs4vYQI0M6dOwE0BejOnTvY3NyEoihIpVJQVRW7du0aufepU7b/OzsENE1DpVKhik0ni7+mabh69SoqlQpOnToVuBhy2BbOw4cP8fbbb+PAgQN4+umnt8SXp1ZqWi/EnRbJ9L8OQpB4KHF6zEiQHF2UBeN/tWpYPxf+1UuBjjWKgjOK5zQIiPgcPnwYMzMzePbZZyHLMv7oj/4I73nPe3D//n189rOfxXe+8x3fmaP79u3D888/jxdeeAGnTxtdydfW1vDyyy/j6aefxssvv4xsNtvPp9UCE5weQtqJWwcqOb88QZtwFotFzM3Nged5RCKRjtxQw4jh6LoOTdNw+fJl3Lx5E6dPnw7Ux22Y3P6ZH7f9H8lEWsSm29hNO4joSBF79wOn6CgJGUpChhgSIMdkXP3x/873MUZxce+0I/p2IxQKYefOnfiN3/gNfPWrX8X+/fuxa9cufOELX8AP/dAP+f5efv3rX8e7776Lt94yRl985jOfwUsvvYSrV6/ipZdewmc+85l+Po0WmOD0CDL2mWbVWOF53taA0ou7d+/i3XffxbPPPosDBw50/EUcRpZapVLB3NwcRFHEqVOntlRrdSlCP9dqgZ7KTOI38akYouNhxHZEzZ/oRMR0wTldcVZ3GkARExdLx3o/Z3E/aXXjPJZe+VHP7ayM2uI+qg1Fh0mhUMDY2Bh++qd/Gq+99hrefPPNjt+3L3/5y3j11VcBAK+++ireeOONXp5qW0brnd2CkFhNpVLxVVvjZxGv1+s4d+4cVldXMTMz0zL6OSiDjuFsbm7i1q1beOaZZ7oSymFw7398BQBQXi8BaO9Gi+2IIz4VQ3zKuwrcTXTaQRMdp9uNcyzQ9Urdl+gMeyGlMYoxnGGfExkwFxSO4/CDP/iDOHXqFL7whS8AAO7fv2/GjXbu3IkHD5wzaPsLSxroAuJCU1XVdxFnO5ea1zRO4hrrRQ2P3+2CLErEhZbNZrF3797A3amHzep/+B9abqOlQwOG0LRD1+ivHREdjjc+L6Us/RjEnabEZVQ27daVIPH2JAKeh65p0OoqeFFAvVLHnZ/7Sez+4l+4n98IutRG8ZyGLTjFYrGjLgPf/OY3sWvXLjx48AAvv/wyDh061IezC8ZoXUpsIUhiQBCxAdxdarqu49q1a7h8+TJeeOEF6ujnQTbTDLpdsVjE7OwsQqEQ9u3bN3JXqX6Qos34GC1uQ4hOtBebdhCxAYBwOtTiTnNitWjI327bSGFDqKqFKjY3N10vGkZxcR/Fcxq24HQ6C4esIZOTk/jwhz+M2dlZ7NixAysrKwCAlZUVTE5O9vRc27H1VoUhQ4q4ymXjqpSWGOAFTTTK5TLeeustaJqG6elp166wg7JUCH5davfu3cM777yDQ4cO4amnnupqOqnf8+o167/8CZTW8gAAXqDvPzoRR3Qijnq5mTBQr7iPFQhCKBVGKNVdrywlHoISN0QzlFAgKgJWf/7jmJ2dxfz8PJaXl1EoFGwFxGxxb8+wz6mTTtGFQgGbm5vm31/96ldx9OhR/NiP/Rhef/11AMDrr7+OD33oQz0/Xy+YSy0ApA/a7OwsTp482dGMGedifP/+fSwuLuLw4cNm12I3Bp3e3G47MuCtWq1iZmbGnCfTaexnlHFLJLBCgvbdEEqFUc6VWrLTAPd4jlrTWgpU1ZoGQeIhKgKe+C+/g+TnXrcNHIvFYigWiyiXy0Npt+8GE8FWyIjsINy/fx8f/vCHARgx4Y9//OP44R/+YUxPT+OjH/0oXnvtNezduxd//ud/3o9TdoUJjg9oA9I6vYInLjXrYj09Pe1r+uQwBMdNOAqFAs6dO4ddu3Zh7969tkViqwnO+i9/gno7id9EJ+KuGWpuuMVv/BBKhaFW6ZaTFJZsNUKA4f6jWVpEdAAg9ws/gz1f/AvbyOWFhQXcunUL169fRywWMyehjnoHiEEzbMHpZNrn/v37cfbs2Zbbx8bG8A//0Hn/vW5hgtMGWmKAKIq+U5ud8DyPQqGAxcVFPPHEE9izZ0/XHaP7tZ1bDOfu3bu4ceOGax+3rSY4VsKZGCrrBfP/XsRrnFjjNwDAi3ZLWVREo4WOI2GBxGZoouOFWq1DkEWs/88/h+RvfdEcuRyJRLB//36EQiHk83lks9mej+IOyqhZN4C9U/QwIBbpdoAJjgektsY5IK3TBVzXdayvryOfz+PkyZOBP0TDblGjqiouXrwIVVUxMzPj2i59KwlO9T99yvw7nLG/HzSx8YrfRMaa21tn5+iajlK2GPjclHjINUuOiA6J2YiKSLVypIiCWrECURFReLiBpOU+8rnmeR6JRAKJRKKno7i3C6qqDt3C2bFjx9CO30uY4FBoNyBNEITAFg6ZxqmqKp588smOrliGGcPZ3NzE/Py8L6usG5ejHx9+L/38pUcbtv+t1g3BzZ0Wm2wKUrvkgXC66RIhNT5+8BIdJ07RCSXD5j4Ijz71Uxj7vT8G4P469mIU93Zi2C617TJeGmCC04KfAWlBF1TrNE6SSt0Jw3KpLS8v49atW3j++ecRj7d3MXVrUbUTk16JjdW6cRKZSKK66W6VRCfirnEW2mRQK0R8StliizvN7VjVfKvoRMaiZh81J0RsAEBTdfACB1Exvu4Pf+G/x8Qf/Klv4aaN4s7lclhbWzNHcRP3WyKRGKr7qR+MguAwl9o2g5YY4IZfC4dM4ywUCuY0zpWVlY7GNpNzGqTgqKpqzvHwcqE56eek0H74+JVk1LRsIhOG08lNbLqN6djrbyKobNpHEhBRcCLHQlTREWTBJjqiIkIMtbq8iOhY4zn42H/o6DmIoojx8XGMj48DaI7ifvjwIRYXFyEIAtLpNDKZDOLx+MilOQdlFASHWTjbCOuAND9FnH7qTNymcQbppeZkkDGcjY0NnD9/HoIg4Pnnn+/78brZrhOq/+lTpjuN5kajEZ1Mol6iz6xxo122GrFE3NxsVvFwEx0rSlxxHavQcm49ck2SUdxkmF6lUkEul8PKygouX74MWZZNC6jdsLFRZBQEp5PCz1HksRccYtU4EwO88BKNdtM4u02p7reFo+s6bt++jTt37uDYsWM4d+5cR8cbdcEBDMsGaAqOILt/HZxiY3Wn9aL4M5QMo7xeMn+7QURHijQzx5xWjrPtDcFq5QDAU//P58H95n/u+tydKIqCHTt2mIFuYiUvLy9jc3MT4XDYFCBrDdCoJpoMW3A6SYseVR5bwWmXGOCFm0utWq3iwoULkGXZdRpnN1X4/RacWq2GCxcuQJIkzMzMdOyLH3ULxyt240SKhiFFu+sA4Iaz6SZJQmgnOkZdkN3SEmTB5o5zEx0lYSxc9XIV9XIVxV/7N0j+1hc7fg5+IK32d+7cCV3XUSqVkM1mcePGDbNtC0lAGEU0TRtqZh5Li97iaJqGhw8fIpFIBOqDRqAJztraGi5evIiDBw96pjAOy6XWjvX1dZw/fx779+83u8l2Sje92/zQj2r08FjCM0nAL14JA876Gy9CyXDP2uaQ/QHG+XE8DzEkm1NDC7/5bxH9tT/s2bG84DgOkUgEkUgEu3fvNotQs9ksrl+/bhakkhTsTppW9ppRSItmFs4WxJoYsLCwgBdffLGj/fA8bwb+NU3DtWvXkMvlcOrUqbZV2sNwqXmh6zpu3ryJe/fu4cSJEz35YHdj4fh5fl2Jzf/9mwCabWh4UUB4zO72JMITnkihXgwWs4mMNZMKdE1D8VG+41P1SomWo4rNyiGpz1ZXH7FyrBlrTjiBB8dzqP/vn4ay07hQUn/yP3Z8zkEhRaixWAxTU1M4d+4cnnjiCWSzWVy5cgWVSgXxeNx0wQ1jrtKwXWoshrMFcSYGdAOxcIrFIubn5zExMYHTp0/3ZDyBF1ah6wXVahXnz59HOBzGzMxMz75U/XSNrays4Pbt20ilUr6zoIJaROEJ//OHwmMJqNXme6Kr9vfWWgwKAKUsPUHBLTstiOgARhzKKjo0sSFWjq5q5pjqam4Tyg4j6C/8xe+ajx2k+Oi6DkEQEI/HEY/HsXfvXmiahs3NTWSzWSwsLKBer9u6IAzC1TVswanX6wPt9tBPHgvBIbGaIIkBXvA8j/X1dTx48ABHjhwJNCBtGC41GuQL3M4F2AndjqamoWkaLl26hEqlgmeffRabm5u4e/cuNjc3EQqFzDTcSCTi+v5q/+cvo16gx0baudOsCQNyvGkFWsXJt3fKAAAgAElEQVTGD+G0caXarvjTmsBgFR3S3saKtbDTCScI0GnjMCyiUy9XIYZkFG8sI7JvD2D5jBHxGYTw0KZ98jyPZDKJZDKJffv2QVVVswvC8vIyVFU1i1BTqVRfilCHLThbLavPi20tOF6JAZ0OM6vX67hx4wbK5TLe+973Bv6AD9ulpus6lpaW8PDhQ5w8ebIvPvJuOw04KZVKOHfuHHbs2IFDhw6hVqshEolgx44dtiA06YRsdcFYi0n5UAgolCAlYqisrVOPHxpPoZY3xIfmTguPJ6FW6CLjtG68IMLjZvE4cbN05Giri4lYOVZhbEe9bHRTKN5YRvgJI4bHCQLQWOyEv/w9AID6E/4TLoLix/tAanzIcD9VVZHL5cwkBI7jbF0QelGEOkzB0XV9ZLP3OmHbCo5bHzQCcYsF+SCRaZyTk5Mol8sdXU0NI0uNUKlUMD8/j3g8junpad/PPahLqpdZaqRLw5EjR5BOp1vupwWh8/k81tbWcOnSJeTzeVy9ehWZTAYTAKRE08WljKdRyzVb24TG3S3V8HiwDKp23QbM/TaEx3RtbdItH0GREFEk1AqU4k9Fhlqxt9+xio2blSPHw0DjM1DLN49bXV2DnEkDlLVa+Mvf65vodJIMIggCxsbGMDY2BsDItFxfX8ejR49w7do1m0AlEomOhGPYzTuB7WPlbFvBqdcNP7bbB4wIjh8fsK7ruH79OlZXV/HCCy9AVVUsLS11dF7dutQ63bZer+Ott97CM888Yxbo+cFvuxnaNkEh23194gWoJfuC/Tbl8d+39hZ1HyQG8OSTT+Ktt97C+Pg4xv6//wN6I/5FrBua2BDrpp8406GJ2ACGCLiJDmBMJbWKjhg2LByn6DhjOVbRIfVHVpSkIcRkH9W1LJTJcYB83gQBnGAsF+KX/wAAUP/QL7R5psHohSUhSZKtC0K1WkUul8P9+/dx5coVSJJkK0L1c7xhZqltJ+sG2MaC06740G97mnK5jPn5eaRSKdMqKBaLHS/83QTUOymoJKOrK5UKvvd7vzfwrBNiVQX5wnXyHL8+8QIAYD1sXEkKYeN4Wr25H71m3+c3MqcB0IXHei7OGJsybrhjrILjRrghRPWSschb3WlB4zd+CaVjVEuG4BQdJ8S6cYoOFU0DeB6aqoIXBEiNbXlRQH0zDz6kgHe5KBO//Ac9FZ1+pLvLsozJyUlzlHKlUkE2mzXjf4qimAIUi8Woxx+mS61SqWyr+UTbVnDa4Udw7t27h2vXrrVM4+zGLdbNFyqoS80qltFotKOU0k7ceEGF8Rt7T0FoCI1acn9POKn52lnF5592TAMAhLCAF298274Nx0H52z+E17LLK/QMIKfYeBEkfuMHq6gIisuCH7a/nzTXmhUlHbclBNDQqnXwjYQF1fK8eQDkFSeWDieJkP72D1H7kX/ruU+/DGJhVxQFU1NTmJqaAgAz/nfr1i3k83lEIhFTgEgCyjAFp1AobJsaHIAJDvU+MvelVqvZRicTunFtdUMQoVtdXcXly5fx7LPPYnx8HI8ePerIF92pReZnm385OuN5v9W6aTkvqVW41ZKKf9oxje+9P2e7vf5ozXU/8lga9Xxr4F6KdJ5MISejqGQ3fT3W6k5rOQcPS0aKhqh92pyJAp1YOYDhWhMU2bhAIsep1wFRhK7WjQQMci49Ep1hjJcOh8MIh8PYtWsXdF1HsVg0i1BJl+ZyuYxKpQJBEAZ+ftupcSewjQXHT7YLTTRI00qvuS+dzMPpBX6ETtM0LC4uYn193exQTbYdlOD4+VISsalvNJ+Pl3VDgxebx7GK07/sew8A4MUb3249F8uVqjyWpu43NJGB6pI+3fLYMSOZQLPW4ui6YU2YJ9e8SPCKzwCt0z+laMgsUnVChqtZEUIy1HKrlSM3WtqA5wNZOcb/xv54RTbiT414EGf5LPVCdEYh/TgajSIajdpGcZ89exaLi4tDKULdTkWfwDYWnHY4rQVScb+ysoJjx4559i4a1kTLdu4tkj48Pj7eUog66NEGbrz9vu9BZb11QVQmJKiV5gLmjNeUH9i3sYoN+Z+T7IvVdw6/iPf99sdRB8yEAQJHEV4hHIIQ9ucvVzIJaDUfrWccr53cCNhXfXaoFkIyBNizyABADBluQD+iEx5LQG13rg0rR4yGzVol4p7jZRngOWiVKngAnCzTRefvv4jayz/n63nRGIaF4wXpgiDLMo4fPw5N08xR3BcvXkS1WrVNQu1HcSazcLYJgiCYmWxkGmc0GsWZM2faXmUN60vhtfg/ePAAV69ebYk3WbftZ7sZP7z9vu+x/R/OKKgq/gLvocnml9kpPgAgJpofZZLhppY0fPN/+q8AgJn/+BLEVBL1DX+uLoI1fiNGwxAbjTytYqN1kDxAhId8ltoVnkqxcIvotOwz4XNholg5UiJmZs+R1HG1bDx3rdoQmkasS69W7aKjNERa17oSnWFbOO3wGsVNilB7PYqbxXC2CcTCsU7jDJIu3C2dXM3RBMc65G16etr1KqtT4ehUqJwQsamsVxHOGK6IasGS8VUJUDS529i+cp8eIBfCvE10QpMSZn/3H/Dib/5Ey2Np8RsaSibpGZAneL5WznRoy/svxyNtZ+24iY4fK0eQRFcrhwhMs/uAYblIceN24lJrnDSg64bgAAAvmNZRYycdi86oWTjtGMQobuZS2yL4+eDeuXMHoijaYh2DgIhd0HiKU3CKxaJZgW8d8uZnW7/0wn144UdeMv8mYuOF053mhrLDWPScNTuAITrW1GopLmDud76ME//mByCmU1Adlo6cSUMtNVxJlviNkhlcy3wS8CfWjhBqvXiQYmHolJhOeCJFFUTXbgMNK8daCOtEq9XBSyKExoKnV6rQYLjY9FodnCQCmtoz0Rl1C6cd/RjFvZ06RQPbWHC8yOfzuHHjBqLRKE6ePDnwqyoS/O8mgE9Stp977jlfvdyGFcO58CMvobxuXH2Hkgqq+fZWghe07DQpLqC2qbbcBjSTCbS6Dl7k8M5/fhPTv9S0dORMo0VKyV+SQCA6fN3keMTTxWaNs3jhFCynlUMTG6eVAxjxL06SwJPMPUGAXjXeU1fRASD9tz9G7ft/qu15msfeYhZOO9qN4hZFsW0RKpkXtF14rATHOo1z7969qNVqXX3AO/2CdGttLCwsoFwuU1O2vY45rKFooWTDhWYRm07daU5I8oBVdIjYkPudojP3mb/EyX/3ctt9S+kktDIp+Gyee7fxG6DVAndmp8nxiGegnyY6zjocktqtUTqMKykji84tA45ArBySdMFJzSWDEwR3S6fhcgsiOqNo4fQyOajdKG5ShJpKpcxR3NvNwhmtd7eHOL/Q1WoV7777LjY2NnDmzBnE4/GuUpu7ufLvtHC0UCiYPt0TJ04ECkp2E8Pp9Hle+JGXEEoEc1U63Wmhcf/bS3HBJjYEZ/q0FJUw//o/uu8nnbSJjRdyMmb+iNEwpFjE8hO1/0TC5k87OFGAGFaoxZ1ORMtEUtr9tu0l0RSbdtD6rwFG0gCs1jlv+VtWAMWe6Sf9tz/2d7wRtHD6KYJkFPehQ4cwMzODZ599FpIkYXl5Gf/8z/+MH/3RH8W3vvUt5HK5wMKnqipOnDiBD37wgwCApaUlnDlzBk8//TReeeUVVKvdeRo6ZdsKjpVHjx5hbm4Ou3btwnPPPQdBELqupelm+04KR+/evYuzZ88iFArhySef7EnCgR86tXCS/9v/glBCQXmj/QCz2I6w+RPZEbL9AIbohMYVqjvNiRgSIIbcRUeOiWZXAJro8D5TW6VEzDP+AUpRpu08LRlv7XCKjnUfrudnETW31jRAq2UFtDYeJRYdH1Kg26y7SjMtWlKARgcCdPi9eNwExwkZxX3kyBG8733vw2c+8xnouo6//du/xfHjx/HKK6/gG9/4hq99fe5zn8Phw4fN/z/96U/jU5/6FK5evYp0Oo3XXnutX0/Dk20tOCSD6/r16zh16pRt7ksvBGcQXZ9VVcX58+fx4MEDzMzMdNy1dpAxnOsf/6Dn/VLEWACjExGEU+4WjKbaF+1wRjF/gNZaHCtW0ZGiEqSoBCXZFBMiOmf/y1c9z7Xl3JMJb6Hxg2XUtBgNUxd9GjTrhdbh2svKkRIxag2S7THJBMRkHGIyDiEWgRiPQYg3nzMfChlWDqFeB9SGEJHvlOO75cfKGUWX2rA6RfM8j+eeew579uzBr/zKr+Ds2bP4tV/7NbMljxfLy8v4m7/5G/z8z/88AEPI33zzTXzkIx8BALz66qt44403+nr+bozWu9tDarUa5ubmzCw0ZwO8bgWnm/Y2fsUqn89jdnYWyWQSx48f72q41KBiOMRUd7rSnMkC0YlWv7RaC5AaTcl2c1o2NEvHChGdi//1TePxKXpGGh8KGUKTTNhShK3FpO1iIV44C045igD5dYMBgEhx2fm1cqRkY9y2w0LTLVYOAAixOHhZgVa1WLBeoiOHIH3rS57n3YtpvL1mmJ2iASNLLRqNguM4PPfcc3jmmWfabvPJT34Sv/3bv22e96NHj2zD6fbs2YM7d+709bzd2LaCI0kSjh49iv379/elPU2/XWrLy8s4d+4cjh49iieeeKLrL+IgYji5XA7LP/sTpkuG5k6LjHUWAOWF1ucfSikIeVhIQKvo0HqXVQt1XPl/v2W7zU/8pte063Tg6lqj3E5rSGq1zGhWjik2PtDrhtjykUYGVaOIGk6XpCQDsr/uDbSJn8Nm2FZX0E4Df/3Xf43JyUmcOnXKvI12wTi04vWhHHUAkL5IbgxbcNwW8Xq9jnPnzmFtbQ0zMzOIx1uvbDsd39yvGA5pC7T2734KSpy+KEbGIoHExulOazkvi1vKS3TkaOuVvW3+TLTR+ZjnsfB//Z3tcWIyATHAIgwAYizqHb/h7V9052wcoNVCsbrIrOLi9rd5KIfocB5WjpSmWHeN56HrxueGWDm2NkGNhp4IhwGy/1DYEJpQq6XlZeU87jEcGkHTor/5zW/ir/7qr7Bv3z587GMfw5tvvolPfvKTyOVyZmeV5eVl7Nq1q1+n7Mm2FRzAW8V74VLrdZba5uYmZmdnMTY2hmPHjlFdaIOup2m3Xb1ex9mzZ1EouFfsRzJNoamVLG6oWu8aoMamogil7FfSRGwkimstlApBSciNxzVF59pf/QsAUIXG6k7jZRlCNGr+iDHjBwDEWMT8EaJh2087+EbaMc0tRvCydNy2EylxJ2LlWOMzQSBWDgDAKkKaw6WmO9rouIjOsBd3GsM+J+JS88tv/dZvYXl5GTdu3MCf/dmf4Qd+4AfwJ3/yJ/jABz6AL33JeN1ff/11fOhDH+rXKXsyWu/uAOn2SqqXLjVd13Hr1i2cP38ex44dw+7duz23HaTgeFk4RCAnJyeR+cP/FUpcQXndXhsSyURQLQwuBdMpOgSa6FghbsB6RTVFBwA0R/W+EI1AiNotNbf0YRpBGoSKkbBrAoCc9BfTCWLlUPFr5Zh/u9QlOURH+O7ftD6EWTgt9Kq1zWc/+1n87u/+Lg4ePIhHjx7hE5/4RA/OLjiPVeFnL+nGwrFuW6/Xcf78eYii6CsLrRvh6EQg3eJNd+/exY0bN8zO2nccM1d4UbBZNu3wShhwxm843ntRCqVCVOtJCgmolVUocbmxH74lBZiw+BffwMGf/D7bbU6hoeLzvRHCIeM9KXunjfOhkGs8iZdlu9XVSIxxiiTNujHvSyWbgslzbdO5W1BCQKVxfrVa061GCkFV1V6zA0BT6FbYsBd3GsM+p24E5/3vfz/e//73AwD279+P2dnZHp5ZZ2xrwennGIFuLBzSqXp9fR0XLlzAU089hZ07d/rathsLpxdZaqqq4tKlS6jX65iZmYEoirj3C68E3i8hOmF8mayC4xwsVnzk3UlZDLV+jOWYTG2jEx0Po15pvm9W0SFtXeoVFaLDa8VHI2YqsO5nLAH8xdqERtaXWq6Y7jQnXqLjB04SbefMSRL0Ws23K01INN2LHNdYfK0iQhIHSMZavQaIkik6uiSDq1WhyyHoFgtG+O7fQD35r83/R9XCGUZaNKFWq/Vl7MGwGK3LiS1EN2nRHMdhdXUVCwsLOH78uG+xIccddAyHLJzFYhFzc3OIx+O2GJPkiE1ExugLmTWhIDYZM8WmHSThwG/SgagYC4Qc8/dFtQbu5aiMUEKBqIi4+uf/CMAuNk5s7rQues4JIaUlc8zq/rJO2LQWp9IKVa1uNCHW/jWzHddiPQqpJASXVHEb5DWIRI1kgXDjtxKG3kgc0BXjPDgPER62NUFj2GnRAIZ+/F6yfZ5Jh3RqAXVa+FmtVnHz5k1Uq1WcOXMmsLk8jBiOpml48OAB3nnnHRw+fBh79+41r0Qf/dLPotwYp+yM3wBoid/EJmOITcbajz12wa9IEayiQ/4mgmRFiYegxEMtty1//bue++dDivnDKbLth9xOw3klz4kCOFGgpjM3j0WP/fCy3HJfa+zGbj2JGfq003aQWA61m0C99T3lyOM0+vttjeWMqoUzrAV/GEMe+81jLTjdusWCbpvL5TA3N4fx8XGMjY119EEedIsajuPw8OFD3L59G9PT00gm3a94I2MxV+smPuWeXhyk4NM4TtPaiU+1dwvRLB2r6IQSii1ORFKyiSje/Kt/Mu/jBKEpMC4uMCdWUfL1eEWmBvd5WYaY8J+m7bRuvM7XauWI6bQ/ywZoJglYvwvktka2mlN0nFYOd+Hrxt0jaOEM+5xGUYS7YbTe3R7T7o0aVANOXdextLSEy5cv48SJExgbG+tLDU+vtyuXy1hcXATHcTh58mSLL/nRL/0sfTuLpROfSniKTTcQ0QmnQgg3stNo1osbzse6iQ7Hc7j3T++4WhiA/0w1qzXk+TgPv32LNRMJU8XMbR8kdhM4Y62BLyvHLVvNgaY0RXEUF9dhC85247F+JUVR7HsDzmq1iu9+97uoVCqYnp5GJBLpWYZbP7d79OgR3n77bezatQupVMp1ISDutFDaf+sVL5wJA0EIu6REA+6uOL/drGulGu7+/bfaPzAARHRorWwA71gNTfysouOWUSem3V1pnCBATBq92czkAD/QrByCi5WjyyGb2HAXvj6Si/swz6larW6rhAHgMRecbvuhtdt2bW0Nc3NzeOKJJ3Do0CHzgzuoxp+dbKfrOq5fv45r167h1KlTSCaT1O2c1g1tYFhsR9MtUy000387jd8406EFqfXj64zDWJHC9it6Oaq0NM60WjlyzNiXILe6oqwWTZA6HCecIjfHNZPbREuyQJsFh28z6qDd9lYrRwjgrvOk3hQVJ1ooaqZFc47anFG1cIaVpVYsFhEO++sovlXY9mnRXnQbw3FbwMmi/ejRI5w6daqlcWi/hY6Gn7ToWq2G+fl5RKNRnD59GjzPo1QqeW5HLBun4MR2JFErth9NEDR+4wURDyUeQmWzmUZsFRopLNm6HZDtnM03Q0nji24VHV4UsPKPb2HXD76v2agSlqt3AHB5rWhD0IBm7ISIDi0bzk003KwczVHb46zX4UTJ3iUgAFwsAT2/AcQTAPl+kbEEZC6OIEBv/K2Fovb7AKMIlGJBnVLW8TCXQzqdHmoqspVhZqltt2mfwDYXnHb0owFnpVLBuXPnkEwmzUWbtu2gLZx2zTvX19dx/vx5HDx40DbGgXa8wu/8e9f9iCEZsZB/N0Bs0u6Ksy78hVX3djntcIqOEznq7kojYkODFwWs/svbGDtz3LjBb+ymYUm4CQ+Bk+WW4kvietMrrWJEamqsiKlky22A0eGZekxJAk+upC3FnxzHN+M11scn2o805zQVOi+Yv1toiA6na9At4pPOLeG7S0vm+OVMJmNOvxwGw3SpbbdpnwATnJ5aGqurq7h8+TKeffZZc46527adCk6vuz7ruo7bt2/jzp07OHHiRMsHvNOC0XZEJ8iI4+Y5Oa2M6Hjz6q4T8XETHadrDWhaOcSioVGv1CEqxldm9VvvYvy9L9gf4ON1so4JoHU54AQBEOjFpZwi20THjAFRRMeJmE7biz8tVg4fjTX7n3nAxRwuN103rBy1blg5Ht0FyH2cqkJvY71MT0+jUqkgm81ieXkZm5ubiEQipgCFw+GBCdAwBYdZONuMXnV81jQN165dQy6Xo7rQaNuOQpZavV7HwsICeJ53bavjFLjC7/x7lB9tUI8RHkugVvCuiI9OJqFSrtTbYRWf4lqRGr9xIoUlSGGpRXSkiGHd1Mv2RTqcjvhy8dXLNYghCbl3LyL1QmOqolNsfLy/TqGwpiaT7gDObDan6DghbjY/ImTfUGiKDsXKsYmNpgE+FuEWK4cIEsFh5aiycbGjLs5BOTiNqakpTE1NQdd1FItFZLNZLC4uolwuIx6PI51OI51OQ1GCjTEPArNwesu2Fpx+x3BUVUW5XMa5c+eQyWRw+vRpX1de3aZj14IsJJZjWi2VfD6P+fl57N2717NZqJ/6HUEWER5zDzhL0RCkqLEQdiI2TiKZSIuIeE3NdLN0xJDUIjrtIFYO2W793CUkjx2yP0jTmvENgvM1JLGbhsVDEwe3uhlaSjVNYFoEzdniRpTA+VisWywbK25Wjtf+HFZOXbHM6XG42IDmqJFoNIo9e/ZA0zTk83msra1hYWEB9XodqVQK6XTaNmisFwzbwmGCs43o1sKpVCp4++23cfjwYWQymUDbduqm6kUMZ2VlBUtLS3j++eep83bcjmeN3SjpOCqNlGgafhIGrO60oJA4C627AUB3m3lB2u4IEu9p5YTThqVFnp+u6e1dadYFi+ZugmGZtAiGbJwTLcDPyXJLgoGQSNCTDvy6ZWhWTpxMAHW8Ju2snMbzdFo5aigKoVyAJkfosR2y+eIchIPT9NPkeSQSCSQSCezbtw+qqmJ9fR1ra2u4ceMGOI4z3W+JRKIrwRh2lhpzqW0jBEFApdJ+YXSiaRquXr2KWq2G9773vQPNle/GpaaqKhYWFlCpVMzGm+2gWTiKS80NzZ0WmfCXrRZkRLNt+FoyjPJ6yfztBrFyiDuN4NfKcSYSyHHjf7VSRe7sJaSOW6wcssDRFmVBMCwC2hRGF2vHmVVGMtpoouO2z+b/TSuHizUsCzeLOd6bNGk1YuyHCIwa9r7IoVk5XgiCgEwmY1701Wo1ZLNZ3Lt3D1euXIGiKKYAkXHNvs99iFlqQad9bgW2teD0w6VWLBYxPz+PiYkJhMPhgRdmdSo4lUoF+XweO3fuxOHDh31/6cjxaq/9OoBmYSaxbsLjKVQ38i3bRSZ8tkbpAaSdjh/RoU0SjU7EUS83F26nlUPLWtNVDZzAm41Lc2cvIXX0abv1QluoyOtOfus6vWmn063UJpWZZJk5RYiLRH1X/duINzLRfCQTELeaFo41z7vxnKzWjRnLIbEbcjt06Gj9PHpZOV5IkoTJyUlMTk4CMGIh2WwWN27cQKFQQCwWM+M/7epchulSYxbONiOo4Ny/fx+Li4s4cuQI0uk07t2718ezo9OJ4Dx8+NC80tu3b1+gbYmFU13L+t4mPJ5EvRTccuwFoWTYs7BUjsq+BsIR0XGKDRlhQFCrNQiyYUUUlm4j+tQTTTHxE1gXpZbhZICRQOAsKOXD4ZbbaFZOy22iZBMdThKNOTYESWpaOVa3mu3gvKtbTY+lbGMHegGna6gqcfTCmRUOhxEOh7Fr1y7ouo5CoYC1tTVcuXIFlUoFyWTSFCCJ0u5nWCnZxWLRVqKwHWCC40NwNE3D5cuXUSqVMD09PdR2E0EER9d1LC4uYn19HdPT03jrrbd6drzwuHEFTLNurFjdadaEgW7iN+0gqc3VvN3FJ4aMxYQmOmJItlk5gHc9DtC0cpyiE3lyt2G1kNeN51uTCABwpGCSWAUN4SGdBqyiQxIIqEIUT1CtGC5iuTp2iI4n8fZ1NgCgJ5pxS07XDdEhRZ0uMRy/Vk5VMdxu5VsLCO094u+8fcBxHGKxGGKxGPbu3QtN07CxsYG1tTXcvn0buq4jlUohk8l4NqodBMzC2Wb4EZxCoYD5+XlMTU3h0KFDLVc7g27H4VdwSAFqKpXCqVOnOj5HjuNw6sJX4Ce3LDxufEH9WDfOrDZrDMdan1LO2gXN2d7GKztNjoVaRMeJtRWOVXTkuOE7p7WtcVo5BLVSg6BIqD54BGksZdTcEHcZyebyguNb3WsUgaHd1mLFeF0UhRuLmNWSIVZOvLHImmJpTSRoWjlWsek1RGwGAc/zSKVSSKUMka3X68jlclhdXcW1a9dQLBZx48aNoRSglkolJjhbiW5jOCsrK7h+/TqOHj1Kvdoh7qZOPoSdbutHcLLZLBYWFtoWoPrBen5ejTXFsP9aiPBECprF7eWVMKAkm1+4ynrnnQeIdUPw61pzQ46HUd0sQYooqBUrEBQJaqW54Nce5QzRITcIgpkoYO2VZsVMg3Z2GqDVRzVEh1Ncar5CjWCz1aoJYuV40FZsAlo5NTkKqVpATY5SkwV6beV4IYoixsfHze/Nd77zHYRCISwvLyOfzyMcDg+sAJUlDWwz3ARHVVVcvHjRHKNM8+tat+90ro2qqoFrBrwER9d13LhxAw8ePMDJkyd70viv/sXfgK6qkJIJVLPrxjl0mCYanmjvqqFV3xOUZBQcz3kKj7PRppeVE51sjTWJIdk26plqTZB9NzLViDUEALwsoV4qQwyHoBVL4OKCkQSgqk2rw6WXWHMnzcJLWD8f7QL4fgQlbLlidsZr4paLKmvMxvI4L7Ex3WoBqIYMS7cq+xt3PWh4nrcVoJZKJaytreHatWsolUqIxWLIZDJ9KUBlLrUtiFfhIm3xJgWRu3fvxhNPPOF5BUMEx02QvOh11+darYbz588jFAphenp6oJk1oYkM6nl3EQhPpHpS8EkgVk9lvQA5HqF2qrYdfyyBWsE9e62TY1vRVRWcIEBQmp8DTjbfC2sAACAASURBVBSgNsSMD4UM64XEYwShRXRaijytomPeZhcILhJt7WggSsaP9X8iQkRsaKIUabixPERNj/mL7bSjFkq0Fnc2YjhuKdGDtHLc4DgOkUgEkUgEe/bsga7r2NzctBWgJpNJZDKZnhSgMgtnmyGKIuqWsbh37tzBzZs3cfToUSR8tGof1AC3dsfc2NjA+fPnsX//fkxNTXV0PjTUP/tsy23KWAq1nJESzSsyQhPuV7xiNAwx2mplaT0aT0A6VRMLgyY8QqMqX4qGqaIjhhWblUP2ZU0g8LJyaPCy4wJE15q1L5JkCpSZJOAWb5Hl1swwp1UiCL4biNJP1iUrDbBZOVo83TKpk4YzeaAeikHnGinSVoFtCItrc88RQNM0zwtOjuP6WoBaLBYRi42m5dcpj7XgEOuH9BQD4LsgEuhPt2k/21kFZ3l5Gbdv38axY8d6/uHUCvYFXBlrf4UbNB3aK34TdBgbbW6NFavoSBYhdIoOQM9ao1k35rk2RESr1sDLEtRK1RA7nodWqYIn7Wg4zsxOM2Mzmm5YNLYTaIgWLR0ZsKc1W0Un1HhelgspiBIgyfb/rVZOxBKkpwiQFg1eAKpGg6dKe1k5ZTmO8r3bSE09EfhcOiVoDY5bAer9+/c7KkBlvdS2IF4uNY7joKoqZmdnzZ5iQYKAw5zcSboG6Lru2njTSVdJDs4F0YLTnaZkjFhAUDeaV/zGD16WDsHN0rFuTyOUSXQ+aI3nTfeZXq0CspESbVo6gF10JMVem+MUnXDURzxHbBUdl/iOLorg6p1ZnU7qseZEUWLtcLoKnRNarBo/Vk5FoicSDIJuiz7dClBv3ryJfD6PaDRqxn9o8VZSpLqd2PaC44au61heXkapVMKLL77Y0RvbrwFuXvA8j1qthtnZWezZswd79uzxLSCkn5ofcdLf+Jzx2/H8iDtNGktBzbcu7ERseo1T8GhpyQQS1xEoTS4Bu3VDoGXZESuHWDbtXGs0KweAad3o1Wpz0Jpap4sOsVw43lt0aK41ycU1F6ZYZg0B0mmNOS371uLpZsIAx3m61erR3r33FYluTeYGaOX0ustAuwLURCJhxn9kWUalUmnbeX6r8ViOmK7X6zh79izW19cRjUY7vooYhkvt/v37KJVKeO6559omNdCO2alF5gd5rHl1a7VubAWfjviNkoxafmLmj5e1QaMlO81jezFCzyayBv07QU4lICdjkJP2z5NWqRoTNzkeHM9Dr1bBywr0xtRQXVWNeI0s20XGeWUfjthdaVarIBRpTt4kOF3DLunYgGHlONF8Ckg9mmwrNpzeSJggcSvN5X/0fvZSp/SzrQ0pQN27dy+OHz+O06dPY2pqCvl8Hp///Odx5swZVKtVfO1rX0Ox6J0UQyiXy5iZmcHx48fx3HPP4dd/3WhHtbS0hDNnzuDpp5/GK6+8gmqb/nv95LETnPX1dczOzmJychJHjx7tKo++m0FqQRd/TdNw8eJF3L17F9Fo1FdSQzfHrD9ao94ujaWo1o08loZabJ8JpqTi5g8ZWeD6WIsYBRUgAJ77d4qO22Odqdy0mhgpEYOUMESGxJ3EsAIpEWvGbgBo1Sq0StUQnXoNvKyAEwTD6rGNqfYQnaALIM26IYfxW7xpETZnXKa90PgXkLIcN3/s+7B/ZnP3bvveZzcMso8aKUDdv38/fvEXfxFf+cpXwHEcvvKVr+D7v//78dJLL6FQ8K5DUxQFb775Js6ePYt3330Xf/d3f4dvf/vb+PSnP41PfepTuHr1KtLpNF577bWBPCca215wiKDouo6bN29iYWEBx48fx65du8z7uxGNQbjUyuUy5ubmEAqFcOLEiY5F0u9YBP2Nz0FIJCA0RE1MeS8qVsvGCyXlXkHuJ0FAjkdM4WknQKSWxikkVqGhWTpBrRwiNDRI12cxFrHV9gCGe81sxkk+Q16i41bgyQvNIk+g1cpxCmTDytEjre+F1cpRfYiRNV7T3Enw71JVjqGsJE1xGhUrZ5ijCUhft9///d/H3Nwc/vRP/7RtTQ6xmgAjYaFWq4HjOLz55pv4yEc+AgB49dVX8cYbb/T9/N3Y9oIDGC/+u+++i0KhgJmZGdsb1+sx037xK1arq6t4++238fTTT+Opp57qyiILLK66BjGVhLpBn/AJwHYF7waxaHqF0nBZEQFqn53mbUk57yeiIzVEzZnmTKwcOZWwxZJI0oNTPLVGSrQQDhsxHouL0VN0CM60aetVtxJqbZlDRIcIkdeiybe+dmqMcoHhCOpTxcYFU0gsbrVKKImqHENF8WepO62cQTDM0QQAbBeHJPGgHaqq4oUXXsDk5CRefvllHDhwwFYTtGfPHty5c6cv5+uHbS84uVwOs7Oz2LlzJ44cOdJyxdKrMdO93pY03lxaWsLp06cDDXjr9JhtCXi1JyfjtmC83/qboNlqtFofJ26i4xbPaYec8rdQWmfbEHHhI2FAEMyOzi1jB8jnUddaxYbgXAidohNytwA1jwLOemKseb4u73ctbvksBsggq4TTqIRSqITcj+/HyinxMaw88N+9vFOGOZqgXq93ZF0JgoB3330Xy8vLmJ2dxcWLF1seM6zu18BjIDj1eh0nTpxwLYgcpoXjtvhXq1W8/fbb0DQNp06d6lnLDD+Co7/xOdsYYi+kDH3hEEIK5KS3RaN1MCbbC2uRqdN9ZZyTjBBlDLYYViCEWhd1JWN/rNXKkZMxW9ZcECsHAPSGhcOFw3YRt36WJNn48Xq/PESlJc04oJXTFQ5rpBxOoxI2LCIOjSQB0+ox/uf19t+jEh9DiR9cmvBWnoWTSqXw/ve/H9/+9reRy+XMAvfl5WUznDAMtr3gTExMeBZPDUtw3LbN5XKYm5vD3r178cwzz7h+4DsZUd3paGshnYaQbrpQeFluERs/CQNuBCnwdKZDc45u0e2snSBNRnuFYKmxINaMXqmaFg6nhAxBUEJGjEUJ2SeC0kRHplhsJF6pGMej1bZooajrfWok2bivKUA2K4cXTFea36LOSqjhnuvgc2e1copC68VCv62cYQtO0F6IDx8+RC6XA2DU/Hzta1/D4cOH8YEPfABf+tKXAACvv/46PvShD/X8fP3y2NbhEEbFpabrOm7duoWVlRWcOHHCUyQ7LeBsF8PR//6LgfZHQ0oloZW9RwK03Ue89cqutum/U7QYDaNuKe6kWTBOhJAMtdFZwGopWS0TXpZsgsXxnCmWHM+3uAKFeAxcw+Ukxo0rc61cBhdSoJeNzgam6JDCTFEyuyzbRhpYx1VbxcZRr6OHoq6Bey2acG+D48PKqUdT9H07a4ZgERofkAJQXlehcUJLE9CSMLhxBVaGLThBLZyVlRW8+uqrUFUVmqbhox/9KD74wQ/iyJEj+NjHPoZf/dVfxYkTJ/CJT3yiT2fdHiY4Q7RwyOJfr9dx/vx5yLKMmZmZth9yIlZBvwxtBbKw2fybLCAerhjV0vpGomSyaVX3+htrdpe1mNLN2iEiVG/ThJO405yiY4W0snFaO1bR6QYxHmtpVaPXVXCiAN5S82WdzKnXa/SxBVbRoVk1AHXBNzdvjANod58ajtmsEJ0XwWmNOiFBgBqKtz0WANN1Rj+g8Vw4aNDBt+0uXRJi0BtOGLcx1CsPstg56T+BIQjDzFLrxMI5duwY3nnnnZbb9+/fj9nZ2V6dWldse8HpdiaOF91aOKqqYnNzE/Pz89i3b59v32ovG3+2EEsA2dYaHJKpJmbGoOU3W+4nuFk3olVgrIH0gK89sT7aCQ95rJfo+MFq5Uix1qFsVitHSra6fXRdM60c48TrgCiCCxnH5xtTOc3EAaeVQ1BCbcca6EqEnFSLKBBXmmezT44L5Ppq13nA3K1LB2gaJSkGXbfExxriNAxUVR3adN/tOJoAeAxiOO0YZtLAxsYG5ufncezYsUCBvG4af7rFcPS//6IhNqoKLhGsRUm7Oh2xgyLVtseMhj1rYKyPc0OgtA2htebhJdEUG4Be/NmCz7gUERouFDGEJhQ2OgQoSuN3CJAt4ujmLgu5L05qxP3113nBsG48qId8vH8c723dOB9OSR4oyG2KSF0y1xbvBWsY65dhutQKhQITnO3IMARHVVXcvHkTpVIJMzMzgVvrdGpZecZwlNaFmUs2FxAxM9Zi3YipJMRUEppLwoCYSAQSm6DdoQFAjIQhRtyz03hJogoL7TbzPh+1RS3nEfcoAG2IhE46YzcyhqyWntlYkzTRNOty6mQnlh06rBeSJGC15h0WhS1JwCKYLWJjnfDKi6bY2NxZln2TY5b9ig3lgqcgp1CQPVKlMfgaHGD4MZzt1ikaYIIzsG4BhGKxiLm5OUSjUSSTyY6GNPV6eBsAoNpdoL/lWJYF3RrL0XuUDu20Mojo2M7BMhjPTWCst9P2AaClRY3z+LT4FYDAVk7baZ2UxVqjXCiYcLy75WM5/27n0RCx8XKb0Qo3C0oKBSVleUzD2uH8vW4FLYKC1r9FediCwyycLUi7GI4oigNrbfPgwQO88847OHz4MHbv3t1RijI5bi8Fpzr/9ZbbuGQaet69wwBHmXLKKTKEZAICJZbhRIhGwSsyhEiY+hMUThQghL07ChBxcYoP1QLyaeX4teB8WTkENyvHuj85RBUbq5WjOsTGKSyurrTGPuqhhD1FmmLleBVxulGUkyjIqWbjTh+tbEwXXOOxRc3+3PvhVhum4GzHWTjAY5A00I5uLRw/22qahqtXryKfz2N6ehqyLKNcLg9tlo4TKXvP+MPluTizp/hkCnrRf5oyQYhGXItKne40IWQP6qtlfwuKEA5BLblba26Wjpd1Q+AV2daWRsqkTQFxHV3gGK4mJBJN66LxW6+Um1lqJGmgkVxgotYBQYQuh8zF3i3LS+c4aI0EAp3jqdZFPWQ8L5Kl5sxm8xO3CSo2RcX/4zlOtyUP2PbTEBu3zLVeMcwstUKhgLGxsfYP3GI89oLTTQzHTx1MuVzGuXPnMDY2hpMnT5rbdCN0fYnhuG2TTAOFvPGPIIBP2hcNEr8REgloldaFnpNECI3Yit8OBq1jlXmb1aO1GexGLB3dY5qoE6eYAJ3Fcqjn47SCSAZa4zdHCj4BQ2QqlZbH6uFoM3bSJlvNC680advjLBlothRpcOCgG3U2FAvdTeAKIe/WTM1pn+6p0u3cZ4v3Kjg41bvC3mH2UmMWzhaln2nR7Xj06BEuXbqEQ4cOtVytDGtaaC1ADMWaNOBGy2KKZusWPhJ2jdm09A8LgNBIaVYbY6Gd3QaARgKBJJqPcdvWtg1FdDhRsp0reYxIcRvSrBwhkaCPkPZCUZoNOK3dnylCQ1ugiXVjbuYQAWLdAHYBIn/X/GSlAb7TqGmWjdc46ZbtNcM1yEOH1keLxgmL4fSebR/DaUc/BEfXdVy/fh3Xrl3DqVOnqKbxMMdT2871G39qSxjwMyOF5k6zWjd8JGw0qPRJJ9lpQFM8OnmM9XbXx/j4wtPEztzeK77j7A7tzFJrh1t6tEK/KiaLuqpEPa0jP2LTrouAVUCCuNEI1uQBIjauj+3jKINhx3CY4GxRvKycXgtOrVbDd7/7XdRqNZw+fdp1RGynfc3Itr2M4WixlNlBmNtoFH06fdcJylVq3NHgMhI1CxkBR4GntXmll3VDcafZjumwFISwAt5RnOdMjyaC4hQWmtDQxi04Y1hixt3yI9lrQipJtWp0v232SaJA4zdn7SDtPKauQ1MirmJj7lKhL2DWZALdZdgaSR6ohFL2QkyP71bRloHm/rxpyQNFLUoVG76NwJy93bslbdh1OMyltg3ppeCsr6/j/PnzOHjwIHbs2NGTfdLoJoZjFbnl5WXsjMSBes1wzSQyTcEhkPiNc1/xBFBq1t+YFfOUOI65TWMxt1oFel31dJJo7cbhNq6meVlu/1gKbqJDbTPjdgqiYIsXCbQ0aZpbzRHLcU0YcEJca43fzmw0180a8RfjpFu7EbSzboIkCfixbNyC/kW9+Xy8kgec+ynUgmc3esFcar2HCU4PBEdVVdy5cwd37txp23izF3Rr4WiahoWFBTyjP2y/EbFsLH3WnJZNuzk5XCgE8MHFQNc1cFZrpc37xMsy3QKQZYiWvmW2bUIhX81GSSyHj3q3iCFuNNOS4bmWepyWdjduNDLTyG9OVW3dm726C7TsSvb+TFbDzTRlW1zHkjyg8QJ4cjt414JMIjZOq6ZdvKagW/rMBcxAs4rN2ds8puQVpNPprlrTMJda73ksBMd5ZW+lW8HheR7z8/MQRREzMzMDSaPsprVNtVrF3NwcpqamIDy8QS021BMZcIV1+k6czy8SBWhWjSCY7iXbQm9t1BkgiwxourZMlxxl8eIaCwxNXDifokNERW+TDWc/N8HmTqRCs3KiMcOKDEebr225ZDTqrJahK2FwlRI0OWRO3XQbjOZGXYk1xYRi5dSU9t2Yy15xG0vyQNCYTRExQ1gCeJedyQP5WquYFotF3LlzB5qmIZ1OI5PJIJlMBhaQYQ0r266tbR4LwfGimw9UPp9HPp/H1NQU9u3b17uTakPQbDPC5uYmHj58iJMnTyKdTkN9ON/yGD9JAwAMd5pjgSXuNC4Uhl7rruuyM9ZhtQhM4XGIrtUaIuLCOa5wraJj7Ybgx9IRkil7/MmjESbH8Z5WDuKJZvwj5rAYI8aVvh4xhEBr0+vMy3KoK50NLLNaOaVQyhQpq5XjpJMEAS/MTDYPt5qbG+2pp57CU089hXq9jmw2iwcPHuDq1atQFAWZTAaZTAaRSGSo0y+9YBYOw8bKygqWlpaQSCT6Gq+hEdSlpus6bt68ibt372JsbAzpdBrV+a/D7TrZtG4Ex8cjlgBKjQw1ytU8F6JUvjutGxKbUFW7u8zaGt+H5cOJAjhR8KzJcYqN9XaapQM0rRvAiDn5tXJ44mZsY3lysUTreGgCieVoKsAL4Oo16KIETlONYD65nbjW2tTjWMXGmhpttXKqSsL8m1ZDU1bcLRurW62gpFsyxmj7I+JYQKtVFcSN1i5ec/Y2j+NPaBBFERMTE5iYmABgLORra2u4fv06SqUS4vE4MplM1+63XsPqcBgADL/upUuXUK1WMTMzgwsXLnRVONqXuTYWrLN2jh49iqWlpdbzaJctx3H2q/Bw1HD7AE13mhICqo2hYhbrxrrou/ZRcxyfEwVwsCcWuEGyytyEh5Mk6nH5WKwlBZmnZBQS0SFC5KzLgeDDlUb25ezCTWbddFHISba1WjmqHPE1DqAq92Zcs1fjTerjHWLjR2isVs4mxYXml3A4jN27d5utpTY3N/Ho0SOq+22YDLPLQT95LASnV2ZzqVTC2bNnMTU1hcOHD4PjuJ7M0+mX4BQKBZw7dw579+7F7t27USwWze2EintrGpIizZccGWqlgiE2VpTGIl21F1I6F2bboh/w9eIcnQqohZ6UIlPS781NdFqOo5AOBV00GLW42axuNS6VbqZ8W6d3uuHXynHglRxgtTgqSoJq8VgfUwqlqY+xutXySsYz5dlp5eS5YAu5VYzchMZNsIiV47pvjkMikUAikTDdb7lcDg8fPsTVq1dRKpVw+/btobjfRtXV1y2PheD4od3I5ocPH+LKlSs4cuQI0ulmHUY3BZz9HKRGfNbPP/88Eo3MKbJddf7r0MJJSJurwQ5MxKbsMfxM1/2lFJPFsl2ho+U9MV1wLhaZl7BY7zOtLlH0VWgppNM2F5xVTP240jhKDVMLxMpxDl7zgSqHoXP2bbziOlU/SQJy8BlGtoQECn7Exk08urFq/CKKIsbHxzE+Pg5d1zE7OwtBELC0tIRCoWC63zKZTF/db7pZ+Lr9RIcJDpqZarRRAbquY3FxEevr62bjTdq2ndBNtpmb4HidLyk2rclRCPUK1KixEIr5LOrRJMTCulnsR6wbLRwDXy5AC0XBly1WUSjcFJ5qBSDdoy0jk4HGVb6qgmvEg3S13lxQdd2+uFqfk3W0sv3JN//+/9l78+hI7vpe9FNVvam175oZjUazaFaNZiRZYxbbhDjECQQ7YOIFg8fYBmzshBCcZJL7ADsmN+YG8uILBN97X4gNODbkBOx38IaBlxwC9nib0TYaSTMjjXb1vnf1UlXvj+5fqbq6qrqqulvSSPqc42ONuqu6qlX1+9Tnu3y+5LuT7IMQi5KbtSIUSCcvbGYUUpVTW79CkDSd39iqdp7S45GpHM7uBJOIgbc5NUc0K0FKNmp5nbi9dsVHTeU9AHJGCxRCIbLRQzRaxQPy7UMsue7Njd0QBAEMw2D79u3Yvn27GH7z+XwYGRkBz/Ooq6sTw28bMfxVDmwRDtQX8EQigaGhIdTX16O/v1/xiWO9WNQAGZeDoaEhVFdXKx6vlnmnRVYGTSqjVMlGChnZgGHEznhpJZkgtdmXqxT5cVHUCrmQ1+RhKJWbXI1sKKtVeXG3WERClIPkZ+SFBpTFCko6c16pYk1rcqpSWE2ucrLhMwDgKjJEIcj+LR6PwBVUOSlb6aqeIpIiATXDTvG9BsNoBGZVzQrZAL+adODaLuOkIw91S8NvnZ2dYvjN4/Hg4sWLsFqtovqprKwsSp3wPL8h1Q2wSQhHz0ycdDqdowb8fj/OnTuHAwcOoKmpSXXbYieGmiUc+WeGw2EMDw9j7969qlVzNE2jY1sLmNDsyi8FXlQ3SlBtLmTjgNWWO7iNEABROXq/F6XvQLoYa+Q7lAwzpSE9uVKhbXbwycKjDopWObX1K02oUpPLAiqH5M/E0QXyhwZ5LkfDXVmKlL2qoLuzAAqJbCFBjlu07D1xq3pILk8FKVSjqYGolEi6Ql3JFHAekJJNMeA4TlO1SMNvQMYV3ufzYXp6uujwWzweR0VFaV0T1gs2BeEUglQxCIKA6elpuFwu9PX1FfzDr1VITdrIurCwgOnpafT09GiOq6ZpGtUxV+ZnPj93ka6sBRNTH7om2J2gErHMP6ySm4hmAFKZJlEB0+8+CZbPWMdU0RmFlBRWtksJmcuPExgc+q/HpQea/+FkUZWcN2ksFRtMOS4vf5STb8kWBchJh67Izo6RlUrTNXU5jbFSlUOR71n699Poy1GEROWIRENARhdkCYXi0znD0JSgpnKSxLKmgLsza6suaIYZs9WsEJFKsQFBBDUF9ydHOG2sMCBn24Tywm5G5Rgt5nE4HCULv21UHzVgi3AArJBGKpXCyMgIHA4HBgYGdF1waxlS43ke4+PjYFkWJ06cKDiuWkvppSvVwx40G80lG7KoJtlcsgEwdeITivuI8JWwUSuLt5RsAODce/8UkZQDg1MOfNr7N/IDz/uZUvjbyMdOa0FJ6Wj150jfg0JPrPJGTg0IxDSVKBUdJdJGVI6eAgGBopGwZt0VckhEWeXoQQTGiw5CaWMeauJ2idLNwCEoxtam2PBbLBbbIpwrGXpm4oRCIYyOjmLPnj1oa2vTvW+GYZBImBtvWwzhpNNpvPXWW2hqasLBgwdLEvOVqhtp3kaQuhBbrBnCoekcspk89vHMy1hRTkTdEESzT682Jn9Rj6Sy458Z4LstX858rgDc43lU+WAVzCfVHAhoZ6Wi8qBtdvU8EOmtIVM41SBXNbX1K/+WHqNCWK2gq0MRKieHaKSFCQoqh7VV6yKTWLZyLYeIFCrTpGRTqHINyCUaPZCSUTnIBiitj5re8Ft9fT3sdvuGNe4ENsl4gkKIRqOYmprCsWPHDJENsDY5nHA4jGAwiD179mDPnj26ySY6/gaYtIQcFRYZzlmTk7cRbJJmSIs10+hJ02LfzeSxj4tkw3LqN3+KWwl1RVMViKYqEExWIpJyIJzMhC0Hp/IbL/+56Ut5vxMT/BStqAakSkcsgdapftTcCUQ4K1emcxYBTbIxoCSQ7YchBJC01+hSNQSsLVuMIPkeFR2cLfqUkpGcDWCMbOTEpUQ2arfCryaVx4SooZzGnST81t3djRMnTqC9vR0sy+LcuXO444478PWvfx3hcBjxuEb7gQSzs7N4//vfj0OHDuHIkSN4/PFMeNrn8+EDH/gAurq68IEPfAB+v78s52MEm5pwOI7D8PAwEokE9u3bZ+qpotiQmhGyEgQBMzMzmJychNPp1Cxm0IKazTznXHkypdkoBJsDdCJz0VNcihz0Ctkc/ljePiLZBUSubghSvPLCH0uqP7k/UfclPFGXIR7FajKKzs/dKBGM/Hc2myIR5TkCFCIYsg+lUJqUELOroSDP15CXNfIr4lCybO5NPiY6Za9C0l6Tfa/C9Sjdd/Y4CNloQaAokWykIS6lEJ7U7VkPCpENRal/H+VSNgSr5RRNwm+dnZ3o7e3Fd77zHRw5cgTz8/O49tpr8bu/+7t49tlnNfdhsVjwjW98A2NjY3j99dfx7W9/G+fOncNjjz2G66+/HpOTk7j++uvx2GOPlf18CmHTEk40GsUbb7yBuro6MdFnBqVwGtADjuMwMjIi9teYuRkStmokHHWgefUQkdK8e4GxZHIG2fDZ6MHb88hGqm4isoVEqm4I0kLm+Mkidm66sAL5ZuX/pXzMVovisDNKqeBDDxEpwWLN9Y/TIiGN/amRTf4bs9eFxrWVctRk/suWO9OC/utQiWyUGkVjTOFcjABKk2yUFJPRMJq4XcKOUMKuSUZKKicYN5Y9KFSlVi7U1NTg8OHDuOGGG/DWW2/hu9/9Lg4cOKC5zbZt29DX1wcAqK6uxqFDhzA/P4/nn38eJ0+eBACcPHkSzz33XNmPvxA2ZQ5naWkJly5dQnd3N2pqajA7O1tUWKzc2xJLne3bt2Pnzp2m8jVLs9OQBosSjlrY47kSm7M6YUlk5t4QdSMwFlDpJKis0hnd81EAQDBZhVqb8nC2eNoKwIpqW25IQK5uCNnEkhZYrVTOOj07l6kqSqczC29LS4Y8/qfjFBIJHn8u/A8AyDUAlboyS0Np8u+YYdRJgfQY6XQhEFFTDqxAKQAAIABJREFUL4a38pDN5fCSAgE1aBUAcI5q8KQKjaJB8xx4WiUHpeQ0kM3lsNbCSiSneEBi0ikIVN5iHxWqJO8tfc4GAMJJR57htl4QsvnpUBX+oEf5mpVjrWfhkKKB9vZ2tLe36952enoaZ86cwdVXX43l5WVs27YNQIaUXC5XWY7XCDaVwuF5HmNjY1hYWMDAwIBo+bJaKsXMth6PB++88w4OHjyIjo4O08UBtnR+PDhZoRLaIUO2smRDQMhGDrXcTThZoaluACCcsOaom9k5FnPz+UUYi4sxLC7GkEhkvq+/p/4il2wIFJROHrnYFeL5hZ5mlXI35N+VCipAtr+8smedSFfWIu2oQrqigNLIklghlVOIbKQkVUjd5Iyg1unybKZAIJxUzr9oqRwCo8qG4Eqc9hmJRHDzzTfjH//xH8W1bb1h0xAOy7J488034XA40NvbC6ukG301VIratloWNZcuXcKlS5dw1VVXoa6u+FkjjKT3RvoUmrJXi+qGs2ae8Kl0KsccUko28XSGYILJ/MUro25WEEo6kOKZPHUTYm0IJ6xgJIvG7BxbkFCXFyNYXowgmeLx1fifKr9JD6EohcQqZedToMw8DypqwwzZcJV1OTm1PGRDbmqzaYD8XI6enA1BnMl9r6CyVCiF0pTIRwBlStmEEuYaIINxiyLZ/HRIX55prQnHaFl0KpXCzTffjDvuuAMf/WjmXm1tbcXi4iKAzDiVlpaWkh+rUWwKwkmn03jnnXfQ1dWF3bt35y1qa6lwlD43nU7j7NmzSCQSuOqqq2C3F5cgXZqdXvlMWf4mZa/OW7R4iw0Cw4BOxHGm7Uac2/H7qvtWIh2CJJe54eNpqxh797OOnAa9s5PmLkH3UgTupQgemPhU7gvW7Hel1MviqMglIz3VZhaLZu5GqKmHKqQkJ60CK9APpUg0hGB05Gnk70lYK8U+Gz2Qk03eoZBQKK9/n2oNnVqQk42SeFVCIFZ8pmCtCUergVsOQRBwzz334NChQ/izP/sz8fc33ngjnnrqKQDAU089hZtuuqnkx2oUm4JwrFYrrr76ajQ0KJeirpXCUSKrSCSCN954A62trTh06FBZL3p5gQBnrQDNJUGnMvmTM203FtxHPFX45k5xuedAUhgRNrMgW60U5ufzO8FJ/objMhukEso5FZF0rDJi1jNjhhAIyd0UmyimzYfSlJpvC84qgkTlKLzXCNEAQJyu0hUeUyIbte1KQTZqkIfVzIbQ5FjrHI4Ra5tf//rX+P73v49f/vKXOH78OI4fP44XX3wRp06dwquvvoquri68+uqrOHXqVBmPWh82RdEAkCkdVKtEWy8hteXlZVy8eBFHjx5FdbWOktUCIxX0IGV1wp4Ii+W2BIP1HxB/9rOVqHdkmkBJOE2KAFuBOkc8J5xG1I0UnKxzPBCmYMuSjZQbClUMEiJKpzLfO8fxuG/sJJ7oUSgflTeIKtm7yM1IpYUGjuxiKSXnbDOoQEZBS8xKpeCJUiGfJzkWafMkoEA2Go4DtMBligc03pOw5ROH1sgCIEM2WiDFA4RstHIopHgglKrUlWshMBtCA1bIpoCDj67igbWqUgMyFbRGFM4111yjes/84he/KNVhlQSbQuEUQjGkQVGU6ZJqElITBAETExOYm5vDwMCALrIx8rm2dFw1f2NPhJHK5m2k6kYPpOomwCovFETdELKRqht/UGa6WSR5fubMLcov2B253m/yz1FxihbJxihUcjlKSFfWatoK5UCjITRpq8qUvVurENcYC60GOdmoqZVCYbScEQGprF2ObouawmSjFFZTy9cUg7VWOFtOAxsYxRKOWRCLmrfffhsURaGvry+nmKHQtnpyR0uz04jZahC3VSMuSxqnrFmrmUQYPGMVyUaqbmKpzELtZysV1Q1BgmPEZjwldSNFOM5g2Zv5eX4hVvAc9IDnMt/FPW/mN6MCyDcEJX83ktORk4786VYeKqvOzd3Ip2/yagl/icJIV2nkf6SbKDxYkCbPhL0arEOZYJTKk5WaQgspG4Io7wQvIRQtIjE6WsCssgnEjLs+BCOF79m1zuFsVC+1LcKBeYuZYhGLxeDxeNDR0YGuri5D5GWmWIHhU2KlUprJkEPKWgGescKSioO3OTHe9D7V7f3xwsULoYQdITazCMjVTSjGIBxnQFFAMJSGzUrBqjAuGlDP3yiF0+S4+42bV/6hZVWjVM1G4HCqkg6ZFaQGrrIml4DMPpQoOgas/C6hQjRalWtSxOkqTbLRW+osR7nJhqgcLbJR+8oJ2Tz9G+0owloTzpbCucKhtZgzDIO0kSa/EmB+fh4XLlxAdXW1qXJFvYQTp3IvXFrgkcj2YpARBZZUpkfnNetvg+X0ze6QhtMS3MrimkxnLqkQa0WYZTL/xTP/EUTZzN+CqBsj+RstcFkyCnoCuPnF6/PJRk3lEKiF1lQgMLKKNQMxfzJtVS+IyklU1IN11Mtey5y3oqJRacLUq2oIovwKifAaRBROOZXLolXU0HpTNgRbhFMebBrC0UIxeRij4Hke586dg9vtRl9fn+mLWg/hnJsJw0olYZGVQieZlSd7R9Zt4DXrb+dtT8JpUvjjdl2VaensQzbH5+ZuQlEKXj8PqzX3vIuakMgRogki4F5xT7j5uWvz30y+b6JulEhHmruRh8oK5Fs4pSZQ2efkhNIKVdJlyYStqEeiQk406teslsoxQjYRvjKHbPIOT0IkqxFGC8QspsqejZANsPaEY6Ro4ErCFuGg+GQ1oO/JnDSfOp1OHDt2DDabrawuBRX0SgEAIyGdilQYKcauSDaeqPKiEU+tLLyB+MrTpZK60YLFArAsh8XFaMH3EmiF0/zLAfhdAfiW8p1wn/2/dynvUKMYQLAbWwSlKodz1spey1c8ugsEskhU1IMlREMMPKH+d9eylYkz1bq80cxAD9lIycks2RDQOirfyG2tRjZaYbW1LhrYqDmcTVMWXc4Z4WTx1yqj9Pl8GBsbw8GDB9HY2Chut9oNp0nGgQo+BXsqmhk7DICsX2yWVDxRJ5w27RBjIG5FXYWyCaiWunH7smE8C62Yv5mb8onkzWV3RBQM+a6ErKkWz/E534Egy3kEAgFUvOuPUPX6v6380qaQt5HV0Qo0k9ujlC2TFnM3ZPiZAgTakldiTpCuWhk7nVMWrTDbB0CeolGCOCtHoeSZeK1REAwTjZaqATJhNTpLbkpko+WpVizZGIFRZUNQ6H4uJziO0108dKVh0xBOOUGq3JQuUDJSYHFxEf39/XA4Vha8YivcjBIOnV3UUowdzqy32lv8iYLbSdWNFIG4FRW2zD4LqZtghEI0xoONc6isXLnsyBo5N+0TiUQPeIViASm++ddOLC0tIRAIIM104v3MUu4bFPpzpLN/5KSjVSggMFbwduUFWq1HpxCkZKNEJhR4VbsZ6TjmOFOl+ppeFDLkVDL0VMNqkk0gXPg8n/5NNe54Tzjv9xzHrZnC2cjYIpwSQG3x5zgOo6OjYBgGJ06cKOkFXIhwpubcefmbJOOAhU/CmQgAAIbpPqhFZzwRG5qq8idzsqmVc0ikKCRSDJx2SQOjTN2Qm56iAIsl8/PiYhQWy8p+5qZ8oAr4lsjVjRTy34XcfjQ370JzczOSySSGhoZwoXkA+xbezN1Q2ohpd2oPPstO6Vz594rK4Sqqc8hJSeWkDRQJaCob6fROGaTERKZzEp7QIig5CqkbgkJhNDlRqZlwakGLbGhKAK9QjKCHaAphrUJqq5VLXitsEU4WFEWZvsiU+nhisRgGBwexc+dOQ/bieqFH4bB8BRjKBgtSSDE2WIRULtkUgBrpyBFLUEilMze5SDiyh/pIlAfHAzZb7verRjbycJoS5OG0ULZg4LnvHgbHcaAoChRFgWEY7Nq1C5ATDtmWqBOZ6iEqR5yAKicd6T7kYTgJklWNK/5mam4D2d+rkY2WS4B0pEHMmhs6k45jFn+noXLUyKZYlWOUbMqpavSgFC4eV+JnlxubRjMW+gOW0t7G7XbjzJkzOHz4cFnIBihMOHE+9wa3CClY+Ax5kLLoRHrlpmYlYbNYcuWykIbT5OqGQI1sxLU0q25CoRSWsurGamEwf9mXd9x6nvCkJETUTUhSnUb6qjiOQzqdhiAI4HkeqXfnN4VKx2lnDpbWfl0KmgFXoZx4FmjjC6aenI0U0uKBmK0WMVutSApKFWxaxQZR3qlb2URSTkRT+kNjwYSxWTarSTb+IIdvvaR83mux6G90hbNpCKcQSmHCKQgCLl68iOnpaQwMDKC21rjFiNHPVMK5mZWYNMvbkRQyDZsMn0bCWoVf+XuwHNL3xOkNFy+CI1Ee4Wjmu7VYlS85PfkbtfcEXV7x51ee6YfNZoPD4QBN05iYmEBDQwM4jkMqlUK0f8WQlM9WpGm5NwtymxqJApaTTd57AaSyM4fEwWmAonM0W1Gv6XOW+0Er30PMVoOYrUZ5rDT5OAXlIVUreonGDIKJ8iobUq1mpjhAbq20HsCyrCHjzisNW4STRbEKJ5FI4MyZM0in0+jvzyx6emHmqaaQwrFRKTAUhyo6Y1JoT2eaLH/l7xHfsxzUd4zesCVH3UhB1I0cYmVahIc/kEI4mILPuzIETkndyCGvTst5jecRdHlzyEYKlmVx9uxZbNu2DXv37oXNZoPVagXDMIhddZNINorILvxE3SgRiQiN11JOZXfyvGPVqWykpBK11SFq084L6VE5MV7/4iaAQiSbt9HT3EmsjggKPVOsZiXaeiQbIBOK3yKcDYByhtQ4jsP58+exfft2HDhwwFAeyGzTqb4cTkbd1KfVR8uyKUY1nMYmV74zX0g5nEaglLsJhDL/cFQwsEpyN0szK2Sjlb9RAs/x8C+5EXR58xTPK8/0AwCCwSDOnDmD/fv3iyN2aZoGwzCi+pFDrnLUQmXZnWmE0jLfZdpRoAw5S2pGw2gAELPXaeZTFB0H5GOheadINoVGQovbGAijycmmEMySjT+8cl3pjYApkY1aWG21EY1GN6zLALCJCKcQzBLO0tISXC4XOjo60NbWZnh7s/00av5vPxtRf+J+LbSibhJZxRKM6e818IVoxdyNHIKQIRuazuRtfF4WrqUILFYaFgsNWqW/QYt4BV6Ab8EN/5Jb8XVCNsvLyzh//jyOHz+uPSV1IH/WDyEdTiFvI1U5aYesRFpLAUnCZDlhNUjIRjqqWSOsFnU0IGZXPyelsJqSyjETQtNLNoJArQrZ+MN0Dtno3k5D2cTj+WPYVxsbuekT2KpSE2GUcHiex8TEBGKxGDo6OgyF0OSfa4ZwaJpGKpXfeNnkjMFGpZASLLBRKVRQMbDWKpzx7lHd13KAQWudvnP3hzL/r3JKrFok6iYY5sFLlAcpELBYM4vt0oxPlXCUwHEcvHP5Ck2qbl55ph+CIGBqagrBYBD9/f2w6BkPPXAj8Ob/m/t5ErIRKFo1NyKfZyNF0llf0ECTddRrJvHliDr0hecIlCrRyGgBGkKeH5pm5ZoK2ShVroUSds1qNV7IHTFglmzMoFAYbWJiAolEAnV1dUin02syE2cjO0UDW4QjwgjhJJNJDA4OoqGhAb29vZidnS2q4MDMtmrKyGFZKWOuoHKt/zUiVVgOMKh2riwU0nBaQqEy2h+S9N6kMz8LAkSyIeomFkshEkrAYmWwPOsDw+QvFkrFAMvTC3mvyZ0EgAzZEH86q9WKY8eOme6fUGveFD+fZsDZVJ70s305qQKhNJ5ixBJpMtAMgObUsJi9TqX5M58k1Mqno5w5b671FkYrRDZqX6OenM2vFt6N+383DJ/PB5fLhXfeeQcWiwWNjY1oaGhAZWVl2SvXNnpIbdMQTqlyOMFgECMjI9i/fz+am5vFbZXUhh6YDalpbRfnHJmFKHtvaqkbVkImngDQZMzEOIdspAgGU7Bale1rCJTyNwsXZgt+JiGhV57pFxs7W1tbsXPnTgNHnkVW5ag6BUhUDmevzO3T0VA5PM2sqBxZf4/c7VnrM6OOBs0KtEKIClVQStHoUTl6yEac7CkhGz3OA6ulbIwWBzAMg7q6OlRWVqK3txcsy8Ln82FqagqxWAw1NTVobGxEfX19WexnthTOJoEewpmbm8Ps7Cx6e3tzLgqGYcCy+idlyj+3VITzzqUEBNjBCzR22BcBAHEh/+JNqFScARnSkYbLpOommdJeRIi6CYfToCggFEog5I/D5rDCuxQAw6jnbxYuzuX9Tkvd/PeHgN/85jdIpVLo7OzEjh07NI9N87gLKBsgSzaAqu8ZAKQqarVnG2Nlhg0hqhyVI4M8jKZX5QBZoikCV5qyUdzGZCWatAHc4XBg+/bt2L59O3ieRzgchtfrxexs5sGooaEBjY2NqK6uLon62chO0cAW4Ygg0zeVQEI2PM/jxIkTeXFdsyqFbFvKkJqNTucsQOO+Vl37SyRXFkpvQEBjnfrNk8p+TUrqJhhMZcNpiWyBgPZCMT9ZWNFI8fLTGYcEj8eDyclJ7N69G5FIBKdPn0ZlZSWamprQ1NRkKKdG9/wO+KGfq76ulcgnKkc0QpVArnIS9gKjwyXxIKM5G4IoqhUVjZLjgOL2BogGAMIJY7nLkIlR0EbJhqIAX8D4PRUIJPHVZyz44h/GFcOyNE2jtrZW7K9LJpPw+XyYm5tDOBxGVVUVGhoa0NDQALvdGAkTbPSy6C3CycJisSCRSOT9nmVZDA4Ooq2tDR0dHYpPMaVoGi12u2QyCQEUWM6GBlsQccGJcV+rSD5K+RtWw7XGGxBylI4edRMMZsKK5CsK+eOgGRruOR9oS/4NbJZsZmZm4HK5cvqdBEFAJBKBx+PB4OAgAKCxsRFNTU26nj61SIezZRSQmCDXUDlauRi9kFeiaRUvSBFFPqFpFQPIw2oRg/NstMhGKawWiFl1jRWQwoyyMUs2BHqLBWw2G9ra2tDW1iZefz6fD6Ojo+B5HnV1dWhsbERtba3uvOJGHr4GbCLCKbjgKCz8Xq8X58+fx+HDh1Ffrx53L6Utjl5IjzccDmNwsQoVlhQabMG892oVC2jB6+fQWJ9746mpG0I2NE0h4IvD5shcWhYrA9pC5xULKIfQ8i1rMp/B4+Wn+8TKwHQ6nTe8jqIoVFdXo7q6Grt370YqlYLX68XMzAzC4TBqamrQ1NSEhoYGQ7F3QjZaSDq0O/0BgBVDafk+atKwWtRer91joxBWi6Eqv3jAoCu0UWUTYm2GJmebmdC5FmQDmDPulF5/u3btQjqdht/vh8vlwuTkJBwOhxh+01Iw8XhcHF+yEbFpCAfQbrKUjpkWBAHT09PiU7RSo6AUxYbUilE4y8vLuHjxItD0bvDCyk0y7mvFvIcWCYHjoBkmI5BXpHn9mRs4nRZQX5dLPoFAKqcEGgCC/jhoCw2fKwKbw5qjbkj+RolstPDy031IpVIYHh5GfX09Dhw4UPABwmq15jx9hkIheDweXL58GTRNi6E3aeWRXOWk7VU5RJJTBpxVOSmlMJlE5fA0g6RNX0xeyzlASeUoKRotKIXVjBINkCEbQNO4Ovt6RuVIyYYXqIIqx2zZcynIBgD+5wsNuKV/SeHd+mGxWNDc3Izm5mYIgoB4PA6v15tTet3Q0ID6+vocNbVVNLBJQJL36XQaIyMjsNlsGBgY0PWkU6zCMUM4FEUhFAohnU5jYGAAQ7Mp1FkzHmoxrgLznvzj9gYEJFMCtjXnvibN3yiBqBm3J5XzOznZ0Nmqs5AvBouVgXfJD5oqrGy08NIPjiMWi2F4eBidnZ1obdWXk5KCoigx9r53714kEgl4vV5cvHgRsVgMdXV1ovoh62c6m5PRCmcl7TUiAam9L2GrzlEs0vdJVU4hm5qc8zFQPKD2WiRdYchFmoCQjV4YVTZmySYQMn4PKZENQSlHE1AUBafTCafTiZ07d4LneQQCAbH6zWKxoL6+Hl6v13BZ9N13342f/vSnaGlpwcjICIDMsMdbb70V09PT6OzsxI9+9CPNCM1qYotwsiB+aG+++SY6OjoMVT0Vm8Mxum06ncbY2Bh4nkdfXx9eHbWgwsqhLntvv34xs3ippRIW3Tzqa7VvqERC/QYmBCSH3xfPMecshmxe+sHxzD79fpw/fx5HjhxBTU1pxiPb7facyqNAIACPx4OLFy/CZmtAd2XuQpRDElmVU1C1SFROIWt/cXYN+bwC749Q+kxh1YjGLJTIRkvlBA0WCKwXsgFKSzhK+ybFBUAmTzw1NYWvfvWrOH/+PCYnJxGNRvE7v/M7BYnirrvuwoMPPog777xT/N1jjz2G66+/HqdOncJjjz2Gxx57DF/72tfKdj5GsGVtkwV54jhy5IjhEtvVDKlFo1G88cYbaGlpgdPpzDw92dKos8cQ4yryxhIA+bNpAMDlyf+lUoOnGrnkhdICLGgK8LsjsFgZ+N2ZXBLJ3yxNL2qelzR/8+L3jgEAFhYWMDk5id7e3pKRjRzk5t+/fz/e9a534dChQ1h26v/7Sxd0uepI2IyFvAp+FkXrJhs59PqlqcGostEiG6WhaWbIJhDiy0I2APCvp/cb3q9ZOBwOHDp0CD/5yU/wvve9Dx/72McwOjqKD3/4w3jttdc0t73uuutE4iJ4/vnncfLkSQDAyZMn8dxzz5Xt2I1iUykcpRyOIAi4cOEC/H4/ampqTC1sxYbUksnCNwCQKQUeHx9Hd3c3KisrsbiYWcRrbSseUK9dUH8ikleauTwcamvyb3QldZNO89n/5y9cAV8cFE0h6I8pOgkUIhspXvzeMXHMQzQaRX9//6rai1RUVGDnzp1Ijs/n/F6qchJ2HUUCWdUiV0byfUWzLgJyKKmcQjkbReeB7O/CKWf+azqHs5WSbJRglmzkoGkq70EobzsdZLOWYFkWV199NT71qU/h4YcfNrWP5eVl0bR227ZtcLnUzXtXG5ta4aRSKbzzzjsQBAG9vb2mhx+Vuw+H+IRdunQJV111lVhmKf/MWFrfwpCSEI/LnYLLnVJUN4UQ8MVFspGaBngX/eobaeDF7x0Dx3EYGhqCIAjo6elZdS8rAtuBdyn+PqlQJCBXOaxN30NLzKZfrRgtEJCi0Cho1e0SNl1kk9OHtUZkU3CbQHLdkw2w8Rs/Ny3hhMNhvPnmm2hvb8f+/fthsVhMq5RiOowLkRXHcRgeHkYsFsNVV10lNpQRtTY8veKXNnTZfHWL253fg0TUjFzd8LyAYCDXWSHgjYJhaAQ9IdAWGjRFg7bQcF3Wp25+/L8PgGVZvP3222hubkZXV9e6G7OblPikqTWDshphtBzbGEmRQKHBa2bJJpSqRCi1koDWM7ZA7X16EIhZdLcg8QK1qmRjFD5PDA9925xdVTEohVt0a2urGP1YXFxES0tLKQ6tJNhUITWChYUFTE9Po6enR3yaWKvFTatKjQwR27FjR55PmPx4E1xuNZC0HFoNiUTui253QiSXmpr8J9ugPxO644WVPhmKphDyRRV90VyXF0EVSL7+6Nt7xGbNSCSC1tZWOJ3OdTHX3XbgXUiOvw4Aik4CasjpsVGoXotZ9SkgARRiMPa0K4bQ0uYXLaNWNYBxu5pAmDLUxwPoIxt5WM0s2awVSqFwbrzxRjz11FM4deoUnnrqKdx0000lOrrisakIRxAEjI2NgWVZnDhxQp+FfZmhFlLz+/04d+6cZtNp9fZMJVck5cDZSw5onU4hpwA5fL4VBZNOcSLByEPkQW9EJIaAOyj+7J5dUiQhKV548iiATCEEAAwMDCAej2N+fh5jY2Oorq5GU1MTGhsby2KUqAd5RCOtPpNVryV09tvoRRTVptQGIRu9ORop5GSjxzhBHkYr1J8TCFO63pezzSoqm7VEMpk0dK3ffvvt+I//+A94PB60t7fjkUcewalTp3DLLbfgn//5n9HR0YF/+7d/K+MRG8Par7iriAsXLsBut+PgwYNr/vRMoBRSm52dxfz8PPr6+jS7kiOpTEXaG+N22HReoykF4kkmNUqgU/lkSMgn5I+CoihQNIWwLwyKokBbaMX5NXK88ORRCIKAy5cvw+fzoa+vD1arFTU1NWhtbc1p1pyZmVFt1iw3Kju7EZ0eKfg+Nq/fRlnlRG21EocB5UICYCWMVqhEWopQ2pwlCiEmM8rGaM6GkI2hbdaIbHhewEPfTuHrD6zeww5FUYZKsp955hnF3//iF78o1SGVFJuKcLq6ukwn9/XATBhIGlLjeR5jY2PgOA4DAwOaCfPXJlfOw2YtzeJLwmlqkKqbkD8q/hz0BPNuEi1188KTR8VzpWkax48fz99eoVmT9MrEYjHU19ejqakpr1N7VSBTOQlrZqE32m+jBjM5G7NkI26vQTZKKsco0QBXFtmsBcwWLV1J2FSEo6eazGzugCTxjW5LQmqJRAKDg4Nobm5GZ2en7v2w6cxiKw2nmcnfSCEWCWTVTY6vGS/kkI0cUnWjlL954cmj4gyblpYW7Ny5U9e52u127NixAzt27ADP8/D7/fB4PLhw4QIcDoeofgrZEJmBlsphbdW6poJGrbUSNUOpqpyYYJw4tMimUFgtyJb++wLyw2VqZKMVVjNDNj5ffvFLwW0KkM1aqJyNik1FOIVA+mnM5HbItkY7lGmaRiKRwFtvvYUDBw6gqamp4DZE3USSVpybovPCaXPzmfwLx61UmW3frpxE1gqnSUE4R0o2FEUh5AuBpmlQFAX/kkdzHy88eRTRaBTDw8PYt2+frnNVAk3TaGxsFE0Oo9EoPB4PRkdHkU6nRZfo2tra8t28FAXWmm9/o6RyYpbiGkC1lFMxysZMCA1Yv2G0cpANzwuiZVO5IQjChlc5W4QjgVlfM7Itx3GGk9tutxvhcBjvec97dHkoSUNpFpqHvLJ9bl75pltYiCGd4rBtu3Jie6X0WVndBL2RvG2CnqAYOvMtukBly3vl4TRSHOD1ejE5OYnu7u6S9hrTIZarAAAgAElEQVRUVlaisrJSdOn1er0lLTxIJpM4547jcPNKPo2QTSGokY2SyokKVYaKBPSSjVzlBBMO1dfU95FRI6tBNr4AZ3iRLwfZrDZSqZShOU5XIrYIRwLiGG3mj260+VMQBExMTCASiaCqqsrwDIxI0orBCQrSNVSNbKRYXIggneLR0qbv8wLeqOJTV8gbyjR80jT8S27V7QnZzM3NYXFxEX19fWW9qSwWC1pbW0tWeEAUWVdXFxDO9DYokY2aypGOHtAavUwmdOotEjCrbKRkY3jbMpGNNKxGHJ+NKIvVIJt7Hvbinx8u79iAaDS6oZ2igU1GOIUWmFIoHD1IpVIYGhpCTU0Nent78frrr+va7mcjDIBMziaepGG1ZgoGLBZgdo7NOT8STlODaymKtGRQDi8qnJUbXlCxCQl6AqKaIcj7N02LlWgTExNIJpPo6+tb1QR/sYUHfr8f4+PjOHLkCKqrq4HGRnjnp3V/fozRWSSgQ9lIicgs2YSTDtBUfml7IZVjZiR0MGJO2RjeZhXIxu8OGf4MM9joowmATUY4hWB23DPZVg9ZRSIRDA0NYe/evaas9oHM06A7QAPZJ+fZuZWeGbkaKVR5BiiTjRoI2ZCwmZq6eeHJo0in0xgeHkZtbS3279+/5slQrcIDu92O5uZmsfBgaWkJMzMzOH78uO5ChJzyZ6a2oMoRKAoxPr/CrdQ5m1DCvEO0mWq01SAbM0QDGCeboDds6nPMYKNP+wS2CCcH5Z7cSab/9fT0ZJ6YDSCjbjKIJWgEghysknLoQou5Uj+NHkgJLOgJ5LwWdHnz3k/RFP79f+1HPB7H0NAQdu3ahba2NlOfXU5oFR5Eo1HQNI1Dhw7lzaZv3NFZUOXoVjZclWqITQlrRTZGpmabIRt/UPnaVAurmSGbgC/jkqHH4JNATjblDqttKZwNBj0htXIQjiAIuHTpEnw+HwYGBorKYURYBoseANkn4Ln5OBhG/02eTuWqGTnIzSgPp2mRDQmn/fj/HIDH48Hw8DDC4TBaW1vhcDjWhU1NIVRWVqKiogLRaBR2ux1NTU1YWlrCxMSEocIDKdnoyeXk/KyhbMxY1aiRjZ6w2mopGzWyUUMxZGMEq6lsCLZyOJsMxQ5SUwqpkQmidrsd/f39pgY7SdUNQwuw22ik0xRcLtYQ2ShBHk6TQhCEPKKhKBohjy/vvWRgGikpv/rqqxGLxbCwsLBubGq0QMJ/dXV1Yh8UGU8dDofhdrtzCg+qFU4hTuuvvIty2u/NydmkKg0pIaD0YbRCKmeLbIpHPB7fCqltJpRa4cRiMQwODhqeIKqGCMuATVJ54TQCEv6S9t8AxsNpYim0jGyAjLKRlz2/9IPjoooLh8Po6+uDxWJBVVUVWlpa8hZthmFyqsXWGizLYmhoCB0dHXnhP4qixDlJ0vHUEHK72Y2QDcnb6IHU7Vn3NjrIRknlmFE1QHnJhoTVSkk2WmG1QmRTzrDaVkhtk6GUhOP1enH+/Hl0d3ejtrbw3BO1sNO/v7kSfqMowB/K3CiLi8rDzrQgD6epFQsE3MrzbEJufx7ZvPx0HziOw+joKBwOB44dO5Z3HvJFm2VZeDweTE5OgmVZ1NfXo7m5GXV1dWUd7auESCSCkZERHDhwQNfcdzKeGoCYy9EiG3lYLc7nk4FaWM0o2RSjagIxc6pzS9mUDtFodF08gJUTm4pw9ORwEglz1S+kwk0QBMzMzGBpaSlnfk2h4yqU56AogE1SCAZTsNnyfcdKgYArAEHFpiWkQEIvP92HRCKBoaEhbNu2De3t7bo+x+FwoL29He3t7eA4Dn6/H8vLyxgfH0dlZaWofsrdBEcaUY8ePWrqRjeiagAgyjtB62zslA9N0+rhAYojm5BOZSMPqxklG6NEA5jzRbsSyQbYUjibDsUqHJZlMTIyAoqiMDAwoPtpnfT/yN8vVTfBCCXesB5P3LC6UYN3yQ+e51V7boB8snn56T4AmSF2o6Oj2L9/f95cdb2QhtcEQUAkEhHn4wBAU1MTmpubS+4QvbCwIDpymyW29m1NmFvUtvMBsnNtssqGB6VIOlJCMTqhczXIRo4rnWykYTWjZHPz5y7g3/9pn+FjK4RYLCaOht6o2HSEQ9SEEoohHI7jMDc3hz179ug2pCQg6kjNw42iAIYB7HYa0roEpYKB2UuZ6jEuGyYj58pL+nE4jgPPrThUq0FONBRNiWTjdrtx8eJF0+pACRRFobq6GtXV1di9ezeSySQ8Hg8uXbqEaDRaEodokmuKRCKr1ogaUwijqYGQje6RBCbJRt7MSVMCeB0WN6sRQgM2l7IhKMW0z/WOTUc4WjBLOIFAABcvXkRdXR06OjpMfa584ZermzQnIBhMw+eLw2LJVzeEaApB6/yk4TS1EBoJGXo8HvT395e14sxms2H79u3Yvn07eJ5HIBCA2+0WHaJJo6aesCWQIddz587BarWip6enJIqpkMpRIhs1lVNI2cjDaqUiG93bmfBF22hkE3Ap5zdLga3Gz00GM4QzNzeH2dlZHDhwAD5ffrmwHmg5HISiFBgG8AeVlQhFUZibNve5BPJwmhLZvPJMP3iex/nz5yEIAnp7e1c1wU/TNBoaGsTQXTQahdvtxvDwMHieR2NjI5qbm1FdXa1IJMROqLm52dRDgRlEeadupRJJ55JHIU+1LbKRbGOCbMzY1UjJphxhta2y6A2IUoXUeJ7H+Pg4EokETpw4gUgkYtqHTd7D893/b+WJnaKAcFRAOJxGZaUFFgudk78xQzZK4TSibtTIhizYjY2N2LVr15o3chKH6M7OTqRSKXi9XszMzCAcDqO2tlbs+WEYRnQ92L17N1paWkp+LEoqJ8pn1IqRiZ16IAgUwklzBpyFyEYtrLbZyaacqkaKraKBTQa9hJNMJjE4OIjGxkZxXHWxBQdKZEVRQCjCg2V5WK00lpaiYjiNYSjMTflyypTFPhyV/I3S8YnjolVKoV/+1z7RMXnPnj1lWbCLhdVqRVtbG9ra2sDzPILBoJj7oWkaLMvi4MGDq3bshGy0IA2rhVNO3Y2dZsjGrKoBtshGi2zGx8fR2NhYsqmzW2XRmwx6SCMcDot29c3NzYa2VYM0pCZVNwBgsVAIhZKorMzNlcxNrSgbrQozNUgJTskT7cl/2A63241f//rXSKfT2Lt3r+mBaasJmqZRX1+P+vp61NXVYXJyEjt27MDc3BympqbKPpxND9lIoZW3kaujLbKRbLMOlM1fP87ga38WwNTUFKxWq+jNZ1albIXUNhkKkcbS0hIuXbqEnp6evAFiRufh6NmWqBubjYFrOQqLNaNuFi77TC+WJJwGKBMNkAmhARlSYlkW+/btQzAYxOnTp+F0OsVS5fU8LGp2dhbLy8sYGBgQCxvS6TR8Pl/OcLbm5mY0NjaamvIqRfu2JozPKzsRq4XVpGRTqM8mmMiMFjACM2RDUwJ8IXO5uc1ENgT79mXyOPF4HD6fDxcuXADLsqirq0NjYyPq6up0q5+tooENCO3mSuX8jiAIuHDhAkKhUM4CJkUpQmpSdROK8LBaKVitFFgWsFjpvPyNvOtfCUrhNK2Baa880w9BEEQXgP7+fjAMI/qKkWR9uftkzIL8reLxOHp7e3NudovFgpaWFtFuhwxnu3z5stgP1NzcvCpx9GhKX9JfAGVqFLRZZeMPb5GNkZwN6Z+rqKjIGX0RCATg9Xpx6dIl2Gw2Uf1UVKj/3bcIZ5NBacFMp9MYGhpCVVUV+vr6VBfVUoXUACAQ4sAwFAKBFGKxNKKRZI660YI8fyOFb8Gd5yQgDce98ky/aDZaVVWFo0eP5pwvRVGoqqpCVVVVTp+MdKBZc3Mz6uvrV92iBoBosVNRUZF37HLIh7MRux1SCNLQ0ICmpiZDdjsHdjh1qZxISn/1mpRseAG6VM4W2ayg3AUC6XQaFJWZfEv+L6+ojMfj8Hq9mJiYQCKRQH19vah+pNcWy7K6Zy9dqdgiHA1Eo1EMDg5i9+7dBTuAi3m6JyG1QIjL/jtjYWO3M7DZGESz71ua8YHKXthyqFXeAYB7din7HvWQ3yvP9Ismljt37tTV8Szvk/H7/XC73ZiYmIDT6RT7ZFYj9JZMJjE0NIS2tjbdFjtSyO12fD5fjt0OCb0Vey4RrZxNXp/N2igbI/NvNjPZAMBNd43ghR8cB8/z4HleJCCGYUQyqaioyLm2AoGAOPjP4XCA4zhR2Zh9UHv55Zfx+c9/HhzH4d5778WpU6dM7afc2HSEo5cYyMJ59OhR1NToG6hlFgzD4Edvd8p+lykWCPrjcDjVmyu1CgZclxc1Xxd4QczXBINBnDt3DocOHUJdXZ2xE0DuQDMlixpCPuUIvcViMQwNDWHfvn0lKWxgGAbNzc1obm4Wz4WEESmKynG6lp+LlsrRIptSYEvZZFBsj41exAKZzyEhdkI6HMeJ/wHIUT8Mw+QM/ovFYvj5z3+Ob37zm5ifn8dDDz2ED33oQ7jmmmt0P9xwHIcHHngAr776Ktrb2zEwMIAbb7wRhw8fNnxO5camI5xCEAQBU1NT8Hg8RQ9L0wvpUw1NUwiFUohGU7BYaFismRyEZyEAii6cv1meXhB/LlS9RshmeXkZ09PTOH78uGaMWS+ULGqIFU48Hi+pO3QgEMDY2BiOHDlSlgcD6bns2bPHdBhRnrNRKyQgKkdN3aiF1UpNNloqxwzRABuTbKQg4TSLxZLxJxQEkYCADDFIw24A4HQ6ceONN+LDH/4wrr32Wlx//fX48Y9/jEcffRS//OUvdT2cvfHGG9i3bx/27NkDALjtttvw/PPPbxHOegfHcWBZFvF43PSwNDN49s2Vzne/Pym6QQf9cZFwCmHx0jwEjSo5eTiN2NRMT08jEAigv7+/6EotNdhsNjGhquQOTdSPUZscl8uFqampkhGlHiiFET0ejxhGzCis3DEHegsECIyG0syQzWqqGsA42fg8McXx0lpYK7L53VvfxM9+OJDzO7J2MAwDq9UqEo9UAZH3URQlEtEHP/hBfPCDHzR0PPPz89i5c6f47/b2dpw+fdrwea0Gtggni3g8jsHBQdhsNnR1da1J0jsYTIFhKPj9LOz2lT/N8qxPrE6TP/EsXJwz/DkvP90n+opZLBYcO3Zs1c5XyR3a7XbjzJkz4jRNUvWmhcuXL8Pr9aKvr2/NJojKw4jRaBQejwdhzzlUb8s8XWqRjZLKCSXsBZtApSpno5KNUaylstEDqapRUj+JRALxuPE8FaCcv10PFaNK2HSEo/SH8Pl8GBsbw+HDh3Hp0iVwHGd6ESs010aOf3g+/0/AMDR8rgjsThu8S/lTNwnmJ2fVj0MlnPby031igr21tTXnyWi1IQ9XJRIJuN1usSRbqVJMEASMj4+D4zgcP358TR4MlCCt4Ovs7MQ708abcYmyKdSTQ1BuspGG1VYrXyMlGzLtsxBWg2y0iEaubgpBrn7S6TQeeOABsafHKNrb2zE7u7IWzM3NiUMC1xs2HeHIMTMzg4WFBfT398PhcJRk6qfR0FQwmMpuTyEUSsBut4CRhNKUZt9okY0cgsCLYwXIhMuuri4xcbleYLfb8yrFlpaWMD4+jqqqKjQ2NmJpaQm1tbU4cODAun2KA4C+TkoX6RCVs9HCaMWSjV6slrJRg1GykSOdTuNzn/sc9u7di0cffdTUPgYGBjA5OYmpqSns2LEDzz77LP71X/+1qOMqFzYt4ZCQEs/zGBgYEBsEV5NwvvI9AUBK/HfAF4fVboHPFQFjZeCe84HOeqdJCwaMhtG+8mBmKqfD4YDX68XRo0fznBLWG+SVYl6vF2NjY2Jz7szMzKo1aZYbRsnGzNC0LbLJoJRhtFKQzf3334/du3fj0UcfNf0AZbFY8K1vfQs33HADOI7D3XffjSNHjhR1bOXCpiMciqKQSCRw9uxZtLa25jkfF9vAadbehmEo0BYafncEDEOrFguokY1awcBLPzgOQRBw8eJFLC4uwmaz4fz58+JifiUs2LFYDBcuXMCRI0fQ0NCQ16RJ/NHq6urWlerRo3LCCeUqSLWw2mqSjS+w9mSjFlbbCGTz2c9+Fvv27cPf/M3fFH3dmik2WAtsOsKJx+N46623cPDgQcWQUikUjh5k1M0KAr446Kx1jVTdSMNpi5fmde2b5G9eyjakTUxMIJ1O473vfS9omhZzJdIFu7m5uWyGlsXA7/djfHwc3d3doiqTN2l6vV4sLi7i/PnzJfVHKxaZa0F9sVcjGzUEYpm8Iq3TWRq4sslGDWtNNo/8acaNg4zAMJrvJWTT1dWFRx55ZN3dc+XEpiMch8Mh5muUsFqEI0UwwMJipRHyxcAwNDwLvjzDP71kQ/DSD44jlUpheHgY9fX1OTkPea7E6/WKhpY1NTXigr0a45e1sLi4iNnZWfT29qpO9WQYJs8fze12Y3p6GhaLRVRyq1U2TUBGWDDNVym+HmJtKLTOSFUOIRsjMEM2ZogG2Dxk87MfDuT48M3MzIjVik1NTaiqqtIkkHQ6jc985jM4cOAAHn744U1FNgBAaVmiKKB0k6TWCIIgIJlUvzmmpqZgt9tNVXmcO3cO27ZtQ319veb7pOomGGBBUwBtWSEcvzuYscbIKpyl6cWCn01Cai9+7xiATBhqeHgYnZ2daG1t1XX8giAgGAzC7XbD6/XCbreLC7beMc6lgLQ/6OjRo6aVSjweh8fjgdvtRjKZXDUlR0rsifOBPKwWYleUTaHDoCghj2z0KBwzZBMIkcF8xm7z1SAbmqbWBdkoIZFIwOv1wuPxIBqN5g0AJEin0/j0pz+NQ4cO4Stf+cpGIhvdJ7LpCAfIXCBqmJmZAUVRpsqFyUCmQvYqhHACvjgomgJNAZEQm0c2QMaehipQ+isnG7/fj/PnzxfdfR+LxeB2u+F2u8HzvNgjU+gprhiQMdYUReHAgQMlK3smowncbjdCoRBqamrERaGUobdwOIyRkREcPnwYtbW1AJBDOFKyAQoTTlAlZ6NFOsWQDWCMcFZL2QS9YcPbrEXps3QAoNfrhc1mw3/913/h2muvxeOPP47u7m586Utf2khkAxggnE0XUisEhmGQSqUKv1EBRooGpGQT9McUS59dlwsrGwJCNgsLC5ibm0Nvb2/RzrNOpxO7du3Crl27kEql4PF4MDU1hWg0ivr6erS0tJTEnoYgnU6LIcBSj7GWjyYgi8L09DSsVqvodlBM6M3n82FiYgLHjh3LKcbo66TwH+eVQ2KCoE46amSjhWLJxtB2G4hstGCkQEA6ALCrq0v0Srvvvvvg8Xiwbds2vPrqq3jf+963qlGD9YJNSThqc2+ADOGwLGtqv3pyOJ//x9wbLuCNir5ovuWArhk3crz4vWNiJVo0GhVn2JQSVqsV27Ztw7Zt20RLF5fLJfbIkLyP2YZZ4lTd0dGBtra2kh67HBRFoa6uDnV1ddi3bx/i8TjcbjfGxsaQSqXE0FtNTY1u0ltaWsLMzIxmvskICpENL1B5KqdUZEPTVEGVs5HIppRNnXJYrVaMjIzg1ltvxRe/+EX86le/wosvvohIJIKPfvSjRe37SsSmDKklk0lVwnG73QgEAujq6jK8XzLIS8senxCOXN0EPSFQNCUShWd+Ofs+7UXkhSePguM4jIyMwOl0Yt++fasq14k9jcvlgtfrzemf0asWwuEwRkdHceDAgYL5r3IjnU7D6/XC7XYjHA7rKqKYmZmBx+NBT0+PZnhOTeXI/1x6lY2UcEqtbLQIZ4ts9CGVSuHuu+9GX18f/vqv/3qjhdGk2AqpmQVN00in06a31Qqpqakb37I/ZzEjZFMILzx5FIlEAoODg2hvb18TOwupPQ0ZZGZELXi9XkxOTuLo0aPrYtqhxWJBa2srWltbc4ooLl26BLvdLuaxHA6HOF2UZdmibHakYbX1EkZTUzlbZKMPhGz6+/vxV3/1VxuZbAxhUxJOoZCa+eZNRrMgQfx8mkLIF1V8zT27VDCs9sKTRwEAoVAI586dWxfKgMDhcGDnzp3YuXOnqBZmZ2cRDodRW1uL5uZmNDQ0gGEYzM/PY2FhAX19fasyBsIopKE3Eo/3eDwYHR1FOp0Gz/OoqqrCkSNHSpLHInY1Rtam1crZmCEaYHOSTTKZxN13342BgQGcOnVqi2wk2JQhtVQqpUoq4XAYU1NT6OnpMbzf5eVlhMNhRRM+qboJ+aMZS3KaQtCTqUoj4TQ54chDaj/81m5UVlaKT909PT1XhFuAIAgIBAJwu93w+XzgOA4Mw+DYsWOr3iNTLDiOw9mzZ0WSjEQieWSqBrWwmlTZ6F2fAmHKEDkBxsiGKJwtstEPQjZXX301/uIv/mKzkM1WSM0sSm1tIwgCLl26BCAzsjnkX1E2AVdukQAZBa2G//PfG3HhwgWEQiFQFIWDBw9eMYs1RVGor69HbW0tzp07BwCoqqrC6OgoBEHIGUuwnm9S0tC5Y8cOMYRJSmHJkDmj/UvyMJpW5RpBIGz8O9pSNuUnm7vuugvvec978Od//ufr+jpeK2wRjgyldBogyfx//PF2ACtEQ1EZZSMtEvAtuDOvqaibF548KlaHkbyI2+3GhQsX1pU7gBZSqRSGhobQ3NyMjo7M0LnOzs6cKZqlnghaSsgbOgmkpbAAxLk4w8PDef1Lv3UwlaNyzORspGSjh5yALbIBtMnmp98/ZvjzpUgmkzh58iSuueYaPPTQQ1tko4JNSThaF0OpCIdlWQwODupK5PuXPJqvv/DkUSSTSQwPD6O5uRk7d+4ERVE5PSXSxHZLSwuam5vXVV4kHo9jaGgIu3fvRktLS85r0ima8omg68UbTamhUw2VlZWorKxU7F+qq6sDqEy4tliy0b2NCbLx+QrnIhW3uwLJ5n891oTBwUEAEIcDGmluTiQSuOuuu7bIRgc2JeFooRQhtWAwiJGRERw6dAgNDQ0A3OJ7iLoh8C26QFHKT/GkOCAajWJ4eBh79+5Fc3Nzznvkie1oNAq32y3eQCS0s5YVYKFQCKOjo7oWa/lE0HA4LHqjlapB0yhIQ2dPT4/h71HevxQIBDBxufBtp6Rc1MhGTeWYbeg0QzZmiAZYe7IhYbTdu3cjmUzC6/WKDwd68nKJRAInT57Eddddhy9+8YtbZFMAm7JoIJ1Oa5LKb37zG7znPe8xvN9YLIbBwUEIgoDjx4/D6XTiU19x57wn5M1c/BRNIejyZn6maPF3BMQ5gJQNHzlyBNXV1YaOJ5lMitY0LMuuiSs0yWuUojhA6o2WSqXEUFV1dXXZzmd5eRmXL1/GsWPHStoZ/vyZwt+F9JQKKRv56fsCnK5pmXKsZ7Ip9UhorZyN1KLG5/PBarWK1xu5jhOJBO688068//3vxxe+8IXNTDZbRQOrDTIULB6P47rrroPFYskrIAh6AnlqRkndELKZm5vD4uKi6e51m82GHTt2YMeOHYqu0C0tLQWrqorB7OwsXC4X+vv7TTsQSFFRUZFXcj0zM4NwOIy6ujo0Nzejvr6+ZOczMzMDt9uNvr6+NQnnCQIQjJggjazjs94RzeJ2q0Q2q2VVU0yBgDwvRx52zp8/jyeeeAIURWF2dhYf+tCHNjvZGMKmVDgcx2k2dxpVOBzHYXh4GDabDeFwGCdOnADP87j3b3zie6Rko6RuyO+JTc3ExASSySQOHz5cckKQlyg7HA60tLSgqampJHkfQRAwOTmJRCJRsh4VLZBQldvtht/vR0VFhRh6M3M+0obOch2/HoVjlGwoKn+8gF7C2SIb/XC73bj//vsRCoUQDodx6NAhfPzjH8eNN95Y1H6vYGwpnNUCy7I4e/as2Ol/+vRp8Dyfo26CnkDONoRs5Hjxe8dEA8uamhrs37+/LE9OpES5vr4egiDk5H0oikJTUxNaWlpM9fdwHIfR0VE4nU50d3evypMfTdNoaGhAQ0OD6vnozWPxPI+xsTFYLJayHv9NvXFN0ilG2RjezgTZBHxxw9tsBLJhWRb3338/brjhBvzJn/wJAGB4eBiLi/qNdjcztghHBYIgFFxs5MUBPM8jmUwiGAzi3i/lkgpRMiGPL+93L/3gOICVSq5du3aV3cBy5RgoVFVVoaqqCrt3786bBkoWaz1GlslkEkNDQ2hra9P0kysnlM7H4/FgcnISLMuioaFBLLmWnw/HcRgaGiqLW7URmCEbf1CZbAqF1TYL2RRLNECGbD7xiU/g937v9/DHf/zH4vXR09NjqlF8M2JThtR4ntccQXD69Gn09/drxu0XFxcxPT0tWtELggCO4+ByubC8vIxH/5+qnPdTFJ1DNuR3hGyCwSDOnTunq5JrtSA3sqytrRXzPvIwUywWw9DQUF6PynoCx3HiTJxgMJhTcs3zfF5D52pArnJKSTYEaoRTCrLRMztno5DNHXfcgQ9+8IN48MEHi3oYYVkW1113HRKJBNLpND72sY/hkUcewV133YX//M//FO//J598EsePH4cgCPj85z+PF198EU6nE08++ST6+vqKPqcSYiukVgxIabQS4ZAxAMFgEAMDA7BYLBAEQcwJtba24sG/zfVJoygaQZc3zyONkA2xtj9+/Pi6cg6QGllK8ySTk5NwOp1i3icajWJsbAzd3d2GK+lWE1Ina+k46kuXLiEej2P79u3ZMva1QTnIRglme2w2q7KJx+O444478OEPfxif+9znila+drsdv/zlL1FVVYVUKoVrrrkGv//7vw8A+Pu//3t87GMfy3n/Sy+9hMnJSUxOTuL06dO4//77cfr06aKOYa2wRTgKUOvFIcUBDodDfMLgOA48z2e80VQuRCWy+e7ftyGRSGBubg6hUGjNKqH0QilP4nK58MYbbyCRSGDXrl3r+vjloCgKtbW1oGkabrcb3d3dYFkWo6Oj4DgOjY2NaGlpKet0UynKSTbSsNoW2RhDPB7Hxz/+cdx00024//77S2embLsAACAASURBVHItkLAvkHHfSKVSmvt9/vnnceedd4KiKLzrXe9CIBDA4uIitm3bVvSxrDbWj2/IOoKSYzTLsnjzzTfR1NSEgwcPAoBYHKBFNiF3/g307//7AFiWxWuvvYb5+Xk0NDSYnjK6FqAoCpWVlWAYBhUVFThx4gRsNhvGxsZw+vRp0e/NYLh21eHz+TA6Ooqenh60tLSgo6MD/f396O3tRWVlJaanp/H666/j/Pnz8Hq9pl3EtXBTb/yKVjZq4bqNQja33357ScmGgOM4HD9+HC0tLfjABz6Aq6++GgDw3/7bf0NPTw++8IUviM7z8/PzOSPv29vbMT8/X7JjWU1cOY+kJUShC4em6RyFQ4oDDh8+LFZ2qZHNH/3JJQC5RCNVNy8/3YdEIgGv1yvmO6TzY0iF2Go9WZuBIAgYHx8XbxqaplFVVSX2x3g8Hly+fBmRSAR1dXVoaWlBfX39uvJFIw2dSj1OVqsVbW1taGtrE/3r3G43JiYmUFlZKZZcl6K3yAzWC9moYa3J5ttfrUMgECiqwZmQzUc+8hHcd999Jb8XGYbB2bNnEQgE8JGPfAQjIyP4u7/7O7S1tSGZTOIzn/kMvva1r+HLX/6y4oPbel0bCmFTEk4hSENqpDigt7c3pziAVLEp/eGVVM3LT2dCcGS65f79+8V8AWlmTKVSOdYa0oqq9bJYk7BiTU0Ndu/enXf+FotlXS/WgLGGTpqm0djYiMbGRnG6qdvtxpkzZ0DTtJgTKmZExJ3XxvC9X+nb3gzZmDXhvBLJ5sWne+Hz+cQGZ1IY0tDQoPuai8ViuP3223HzzTfjs5/9bFkX97q6OvzWb/0WXn75ZTz00EMAMjmeT33qU/j6178OIKNoZmdnxW3m5ubWZNhiKbBFOApgGAbpdBqTk5MIhUKKxQFKBHDD7W8r7o+QDbF5UZtuKX+y9vl8WFpawvj4+LpwhE4kEhgaGtJdyaW0WLtcLpw5c0ZM4Le0tMDhcKzC0a8UfMRiMfT29homcel00z179uSVkJfbOmi9kg2ZDrpefNFaWlpEY9tQKCQqbqlPn1pPFiGbP/qjP8KnP/3psvwd3W43rFYr6urqEI/H8fOf/xx/+Zd/KeZlBEHAc889h+7ubgDAjTfeiG9961u47bbbcPr0adTW1l6R+Rtgk5ZFA9CczDk5OQmv14v6+nrs378fgL58jRLhvPJMPwRBwOzsLNxuN44ePWq4+13qCO31ekvuDKAHkUgEIyMjOcqsGMTjcdHnbTWS9NKGznI01BLrILfbjVAoZPgBoZDCWa9kQ+B3qxOB6uescs6GZVnRiy+RSKChoQFNTU1iBCEWi+G2227DrbfeinvvvbdsymZoaAgnT54UC45uueUWfPnLX8Zv//Zvw+12i16MTzzxBKqqqiAIAh588EG8/PLLcDqd+Jd/+RdcddVVZTk2k9D9RW0Rjgwsy+L06dNobGxEd3e3Zr5GCjWy4Xke4+Pj4Hkehw4dKklojFSIeTwecUyB1FSw1CBuyd3d3WJ1TSlBLPzdbjei0Sjq6+vR0tJSslDiajd0yh8Q9A5kUyOdLbLJoJQFAqQny+Px4Bvf+AaWl5cRiURw++234/Of//wVmyNZI2wRTiEkk8m8ZFwgEMDo6Khof79z505dZAPkE84rz/QjlUpheHgYDQ0NZVvoWJYVlUI5ig4WFxcxOztbcrdkNZC8j8vlQiAQQFVVFVpaWkzPw1Ga0LnaiMVi4t+IDGRraWnJm26qRDirRTZmiAa4MslGjnA4jE9+8pOorq6Gy+UCTdO4/fbbcd999xW9702CLcIpBDnhLCwsiDb0gUAALMuio6NDsziAQEo2rzzTD2Cl837Pnj15A8fKBVJ04HK5ii46EAQB09PTCAQCOHr06Bq5JWfm4bhcLni9XnEeTnNzs668j9qEzrUEmblC1Jz0b/SDX+eqxy2yyaCcZBONRnHrrbfijjvuwD333AMAcLlcmJycxHvf+96i979JsEU4hUAIhzgDh8Nh9PT0wGKxYHl5GXNzc+jq6tJl+EgIh5CNz+fD+Pg4jhw5gpqamrKehxpI0YHL5UIwGDSUU+B5HufPnwdFUThw4MC6qZAjeR+Xy6WpFABjEzrXCtIqPr/fj6qqKpwJZPoxtsgmg3KSTSQSwW233YZPfOITuPvuu03vR82qZmpqCrfddht8Ph/6+vrw/e9/HzabTZyj8/bbb6OxsRE//OEP0dnZWfT5rCG2CKcQUqmUOLbZ6XTmFAek02ksLi7C7XYjnU4bSmjPz89jYWEBPT09qxKC0gMjRQfpdBpDQ0NlDQOWAqlUSgxTxeNx1NfXi0ohEAhgYmJCtRpwPYJU8X33P80psS2yMYZIJIJbb70VJ0+exF133VXUvojzhtSq5vHHH8c//MM/4KMf/Shuu+023HfffTh27Bjuv/9+/NM//ROGhobwxBNP4Nlnn8VPfvIT/PCHPyz6nNYQW4RTCKFQCO+88w46OjqwY8cO1eIAaUI7FouhoaEBLS0teaWvRCnFYjF0d3evWemyHkiLDqS9JBRFYWhoCB0dHavmVl0KcBwn5n28Xi84jkNXVxfa2trW9d9BCTzP45svGiv+2CIbYyBkc9ddd+HkyZNF70+KWCyGa665Bt/5znfwoQ99CEtLS7BYLHjttdfw8MMP45VXXsENN9yAhx9+GO9+97uRTqfR1tYGt9u9bh/udGDLvLMQLly4gIMHDxZ0DpDOpCeVLaSpjLgn19bW4ty5c6isrERPT8+6v3AqKyuxe/du7N69Wyw6GB4eRjgcRltbGyorK3WNZ1gvIP0V8XgcsVgMu3fvhs/nw5tvvqm7Qmw9gFTTAe/Svc0W2RhDOBzGrbfeirvvvht33nln0fsj4DgO/f39uHDhAh544AHs3bsXdXV1Yu5TakcjtaqxWCyora2F1+tdN3nGcmLTEs7Ro0fB87wu5wACqdswcU9eXFzE4OAgqqur0dbWpuoyvV7hcDjgdDrB8zyuuuoqxGKxHKcDUp68nslH2tDZ19cnNpx2dXUhFovB5XJheHgYgiDk5H3WE1KpFAYHBzOVdDptsjYa2ZRzcBqQIZtbbrkF99xzT0nJBsi3qhkbG8t7D7mHNpJVjVFcOStjiUFRVEHnAC3QNA2GYUSnZ4Zh4HK5MDU1BbvdLvbGrFZjplmQnFNfXx9sNpvYxUyKDhYXF3H+/Pl14XSgBGlD59GjR/NuXKfTic7OTnR2diKZTOoexraaSCQSGBwcRGdnJ1paWvD57Qk8/lNtNbbRyEYL3/3GNrAsW5QjBSGbe++9F5/85CdLdmxyEKua119/HYFAAOl0GhaLJceOhljVtLe3I51OIxgMrulYjNUE8/DDDxt5v6E3r2eMjY2hqqoKNE2bqsJaXl7GhQsXcOzYMVRXV8Nut6OhoQHt7e2oqalBKBTC1NQUlpaWkE6nYbfb15Xykc71OXbsWJ7PFEVRcDqdaG5uRnt7O2w2G3w+Hy5cuCA6JzscjjUlHxKCqqmpwd69ewuSBsMwohIl1iBLS0u4ePEiQqHMoupwOFa1Ki8ej+Ps2bPo6urKCamcnlC/VlaLbPzuENiYiSFtJQyjPfcvRxCJRHD58mXMzc2BZVlYLBbYbDbdDwmhUAi33HILPvOZz5SFbEgPnMPhQDwexyOPPII//MM/RDAYBAB0d3fjb//2b/G+970PAwMDCIVC+NnPfoY/+IM/wI9+9COwLItbbrnl/2/v3sOirPP/jz8HQZREzhBJCogiKiKKC3kKE/IADFkooG24ZLmVhevXTpd1ZdduaLWZmu5ua5nutmXtcjCTSLO82GyVVcETKChggOhwTAQ5zdy/P/rd9wKBcpgZBvw8/gvxns+E3K+57/v9eb/1vi4jer2r33hHFg1IkkRcXBxZWVnMnj2biIgIpk+f3qVAkPenVFdX4+vre9uGgPIzEo1Gg1arVW7JGWLHflfpdDpycnKwsLDodpsXuSJHrhBrfZvRmMPj9Lmhs6MqPvk9GfIKta6ujtOnT3dYut3ZFY4xw6YnDPnMRt5nVl5ernQid3R0xN7evtMPPnLYrFy5kmXLlnV7bV3RWauagoICpSza39+fjz/+GEtLSxoaGvj1r39NVlYW9vb27NmzB09PT4OszUhElVpXNDY28s0335CcnMyxY8eYNm0aERERBAcHd3j5Lp+o5X5c3f0kLJfyajQaGhoalHLr4cOHG+2WTnNzM6dPn8bJyYmRI0f2+niG7nTQEUNv6GwdqIASPvp87nP9+nXOnTuHr69vpx8+2ofOnRw27bWeQFtdXa18SHB0dFSKQ65fv87ixYt5+umniY2N7fbahC4TgdNdLS0tfP/99yQnJ/Pdd98xbtw4IiMjCQ0NxdramitXrnDixAkmT57cZhhST8nNHjUaDbW1tco+EkPOjbl58yanT5/Gw8PDIN0P2vdEM0TRgbE3dDY2NlJRUYFGo9FbR2i5N52fn98trwpbB05Pwqaqor7TAWmd6Q9h0xH5Q0JFRQUbN27E3d2d48ePs3r1apYuXdrt4wndIgKnN3Q6HSdPniQpKYmvv/6a4cOH8+OPP/Lqq68SHR1tkNdr3T/M2tpa6R+mr2ckP/30Ezk5OUY7Ucsl5OXl5UqnA2dn51ve/rgd+UTdVxs623eEtrGxUWatdPU9lZeXU1BQwOTJk7tUpr3lS8seh42sq6HTX8OmvYsXL/Lcc8/R2NhIfX09s2bNYtmyZdx33329PrbQIRE4+pKens6aNWt48MEHOXbsGEOHDiU8PBy1Wo2rq6vebxvJMzzkTYxDhw5VugL0dGiZfJKbNGmSUZ+zyORnJBqNhqqqKoYOHarcpurqe5IndBqriejtSJKk3NKprKxUCixuNTKirKyMkpISJk+e3OX3/frH3f/31TpsoGuBM1DCpqamhsWLF/Pcc88RHR1NU1MT//73v2lqamLBggW9Pr7QIRE4+nD+/HmeeuopPv/8c5ycnJAkicuXL5OSksLevXtpbGwkLCyMiIgIvLy8DBI+rbsCmJubd6t5JUBxcTEajYZJkyb16ZRNWU+KDuT34OfnZ1KVfrLW70keGdF+Eqg8D8nPz69bV3jdDZz2YQO3Dxxjlj0bI2wSEhJ6VfVVXFzMY489xtWrVzEzM+PJJ58kISGB9evXs2PHDpycnABITExk4cKFAGzYsIEPP/yQQYMGsXXrVubNm9fr99OPiMDRF61W2+EJQpIkNBoNe/fuJTU1lWvXrhEaGkpkZCS+vr4GeQ7TunmlJEm3fJgtSRL5+fk0NjYyYcIEk2nA2V77Kj5HR8c2VXzyhs6JEyea7HtoT54EqtFoaG5uxszMDJVKhb+/f49uJ3Y1dDoKG1lnoTOQwiYqKorf/e53LF68uFfHKisro6ysjClTplBbW8vUqVNJTU3l888/Z9iwYcooaFlOTg6xsbFkZmZy5coVQkJCyMvLM6n9agYmAsfYampq2L9/P6mpqVy4cIHg4GDUajWBgYEG+YfX1NSknNQaGxuV6jBra2t0Oh3nzp3DysqqS/tTTEX7ogNJkrjrrrsMFuCGJkkS58+fp66uDktLS6WUV37u09X31JXAuVXYQMeBM1DCprq6msWLF7NmzRqioqJ6fbz2IiMjWbVqFUeOHOkwcDZs2ADAyy+/DNCmV9odQgROX7p58yYHDhwgOTmZEydOEBQUhFqtZvbs2QbZ19HS0tKm4q25uRlXV1fGjBnTb8KmNa1Wy6lTpxg8eDBmZmZ6KzowJrkDgoWFhfJzaF3KW1VVxV133aU897nV7c7bBc7twgZ+GTh93RcN9Bc2UVFRrF27lkceeaTXx2uvqKiI2bNnc/bsWTZt2sSuXbsYPnw4AQEBvPPOO9jZ2bFq1SqCgoJ49NFHAXj88cdZsGCBQcLPRInAMRXNzc1kZGSQlJRERkYGvr6+qNVqQkJC9F5pVV9fz6lTp3BxcaGhoaFfnqg72tCpj6IDY9LpdJw5c4bhw4fj7u7eYejL4wjk5z63e5bVWeh0JWxkcugMlLCpqqoiKiqKF154gYcffrjXx2vvxo0b3H///axbt46HH36Ya9eu4ejoiEql4tVXX6WsrIydO3fyzDPPcN9997UJnIULFxokAE2U6BZtKiwsLJg7dy5z585Fp9ORmZlJUlISb775JqNGjSI8PJyFCxdiZ2fXq9epqakhNzeXiRMnYm1tDbQ9UV+8eJG77rpLqXgzxYfvnW3oVKlU2NraYmtr2+YBfVZWlnKidnZ27lWvLX2R5wk5OTndcr+WSqXC2toaa2trPD09lWdZubm5ygZaJycnrK2tO71K7U7YyEwhbNL//6DC3pDD5sUXX2TRokW9Pl57zc3NPPLIIyxbtkwJMxcXF+XPn3jiCcLDw4H/9UaTte6bJrQlrnD6iPycJSkpibS0NGxsbAgPDyciIgIXF5du3Qq7du0aRUVF+Pn5dXrSlT9RyxVvFhYWSoNRUygz7umGzo6KDjqbAmpozc3NZGdn4+bmpvRq6+lxWrdwsbOz47PjPm2+pydh81Nlbbf/jr7DZuvr1lRXV3f5dmJHDB02cusre3t7Nm/erHy9rKxM+bm+++67HDt2jD179nDu3DmWLl2qFA3MnTuX/Pz8fnFHQU/ELbX+RJIkCgoKSE5O5osvvkCSJKXc2sPDo9MTp1ymXVVVpYzH7iq5bb/cvsXZ2RlnZ+c+2aejrw2dctGBRqOhvr5e6QpgjG7QjY2NZGdn4+npqZTN6kPrMdRy6PTXsJFvo7W/ndh6CKBcRt6ZyspKoqKiePnll3nooYe6vb6u+P7775k1a1abYpXExEQ+/fRTsrOzUalUuLu78/777ysB9MYbb7Bz507Mzc3ZvHnznbbnRwROfyVJElevXiU1NZWUlBSqq6uZP38+arUaHx8f5RdAp9ORl5eHVqtt8/WeaF/Ga4x+aDJDbeg0RKeDztTX13P69Gm8vb17fWv0VhI292y8gCmFTUfkf3/l5eW3bB8kh826detQq9XdXp9gMCJwBorq6mr27dtHSkoKhYWFPPDAA4SEhLBx40YSEhKYP3++XkOhfWmy3GC0N73DOmOsTakdFR30tnuD7MaNG5w5c4YJEyYwfPhwPa24c90NHVMPm/batw9qamqipKSEGTNmsHz5cl555RURNqZHBM5AVFdXx6effsq6devw8PDAz8+PyMhIZsyYYZATtnyVoNFolN5h8lVCb66oWk/oNPaGzvbdG3pTdPDTTz+Rm5tr1N5u3Qmc/hY27cn7mLZs2cLBgwcZOXIkK1asIDw8vFfPyAS9E4EzEOXm5rJs2TI2bdrE9OnT+e6770hOTubIkSP4+/sTERHB3LlzDfIcRt5DotFoqK6uZtiwYUqD0e48O5L3pwwaNAhvb+8+3yfU06KDyspK8vPzb9vxWd+6Gjj9PWxk5eXlREVF8dprr+Ht7c2+ffvYt28fW7duxdfXt9fHF/RCBM5AlJeXR0tLC+PHj2/zda1Wyw8//EBKSgqHDh3Cy8uL8PBw5s+fb5DO0JIkUVtbq1wldHWktjyh09bWttP9KX2pq0UHGo2GoqIiJk+e3CcjxG8XOgMtbNavX09YWFivjycYjAicO5VOp+PUqVMkJSWRnp6Oo6MjERERhIWF4eTkZJCTfOtbVHLFUftbVPqc0GkMnRUdNDY2cvXq1Q7HchvLrQJnoIXN66+/rjTI7KnOmnFWVVURHR1NUVER7u7ufP7559jZ2SFJEgkJCaSlpWFlZcWuXbuYMmVKr9/TACYCR/hfA0+53NrCwoKwsDAiIyNxc3MzSPh0NFJ7+PDhXLx4kdGjRxtkQqehyaMILl26xPXr17G3t8fFxUUvRQc90VngDJSw0Wg0REVF8fvf/14v5cWdNePctWsX9vb2vPTSS2zcuJHq6mrefPNN0tLSeO+990hLS+PYsWMkJCRw7NixXq9jABOBI7QlSRKlpaWkpKSQmprKjRs3WLBgAREREYwbN84g4dPc3ExxcTFFRUXKbTdjj9TWB7nI4ebNm4wfP56bN2+2KTqQbycas9NB+9AZKGFz7do1oqKieOONN5g/f36vj9cRuRnnqlWrOHz4MK6urpSVlREcHMyFCxdYuXIlwcHBylhqb29v5fuEDonWNt2Vnp5OQkICWq2WFStW8NJLL/X1kvRKpVLh5ubGs88+y7PPPktFRQVffPEF69evp6SkhJCQENRqNf7+/nqrGpM7GwQGBjJkyBAqKyspLi422khtfZAkiQsXLiBJEhMnTkSlUjFs2DCGDRumtKTRaDScO3euzzodiLDpuqKiIrKysggMDOTatWtKiLi6uqLRaAAoLS1t05bIzc2N0tJSETh6IAKHn+/XP/PMMxw8eBA3NzemTZuGWq3+xcP5gcTR0ZH4+Hji4+Opra0lLS2Nbdu2kZOTw6xZs1Cr1UyfPr3HPdfkDZ3+/v7Khk75Cqf1SO28vDyDjNTWB51OR05ODkOGDOl0zMOQIUMYOXIkI0eOVIoO5Kshe3t7g+1hkg20sElMTDTY8LIbN27wyCOPsHnz5lvumerork9/uiI3ZSJwgMzMTLy8vPD09AQgJiaGvXv3DujAac3a2pro6Giio6NpbGzkm2++4V//+hdr164lICAAtVpNcHBwt6eM+vv7d/iMw8zMDAcHBxwcHNqM1C4oKDCZTtBarZYzZ84oFXVdYWFhgaurK66urkrRQWlpKbm5udjY2ChzcPQRqltWD2X5q5pu/z19h832P9hSU1PTq1C9evUqixcvZsOGDTz44IM9OsbtdNaMU+6PVlZWhrOzMyCacRqSCBw6voS+Ux8SWlpaEhYWRlhYGC0tLXz//fckJyfz2muvMW7cOCIjIwkNDVU6UrfWekNnV2/NqVQqbGxssLGxwcvLS6l4y8rK6tFIbX1oaWnh1KlT3H333YwYMaJHx2g9bkAuOigvL+fixYtYWVnprdNBd+g7bL76ZAqVlZVKqPakfZAcNhs3biQ0NLTb6+sKSZJ4/PHH8fHxYc2aNcrX1Wo1u3fv5qWXXmL37t1ERkYqX9+2bRsxMTEcO3YMGxsbcTtNT0TgIC6hO2Nubk5wcDDBwcHodDpOnjxJUlISmzZtwtXVVSm3dnBwoKmpif379+Pj44Ovr2+P/v+1fz4ij9Q+e/bsbUdq60tTUxPZ2dmMGjWqTTv63lCpVNjZ2Sklt61D1VhFB4a6jSbfJm3dPujSpUsMGTJECdXO9irJYfPmm28SEhLS7fV11ZEjR/j73/+Or68vkydPBn5uxvnSSy+xZMkSPvzwQ0aOHMk///lPABYuXEhaWhpeXl5YWVnx0UcfGWxtdxpRpQb85z//Yf369Xz99dfAL0fGCm1JkkRubi7Jycns37+fwYMHU1tby8yZM0lMTDRIEcCtRmrr68NBQ0ODMo/HwcFBL8e8HTlUy8vLe1R00JXban3xzKb13iyVSvWLbtBlZWUsXryYt99+m7lz53Z7fYJJEWXR3dHS0sLYsWM5dOgQI0aMYNq0aXzyySdMmDChr5dm8ioqKggLC2P06NFcuXKFxsZGZbSCl5eXQa4UW4/UvnHjBvb29krFW09fr66ujjNnzjBu3DhsbW31vOKuaW5uVsKnq0UHtwscUygQaN2NfO3atYwdO5YTJ06wefNmg91GE4xKBE53paWlsXr1arRaLfHx8axbt66vl2TydDodDzzwAC+++CILFixAkiTKy8tJTU0lNTWVa9euERoaSmRkZJvZIvpeg9xgtKdjCOThb62npfa1jhqndlZ00FnomELYtJeXl8eqVauwsrKirKyM6dOnExcXx/Tp03t9bKHPiMARjKOurq7TZyo//fQT+/fvJyUlhQsXLhAcHIxarSYwMNAg5c+tnyNUVlZ2aaR2TU0N58+fZ9KkSbcd/tVX5KIDebxC+2mZHQWOKYbNlStXWLJkCe+88w5z5syhpaWFI0eO0NzcbNBnOILBicARTMvNmzc5ePAgSUlJnDhxgqCgINRqNbNnzzZIA8yujNSW98zcajS3qWk/LXPQoEG8l3pvm+8x5bDZtGkTwcHBvTpWfHw8X375Jc7Ozpw9exaA9evXs2PHDmXaamJiotKDbcOGDXz44YcMGjSIrVu3Gmyfzx1MBI5gupqbm8nIyCApKYmMjAx8fX1Rq9WEhIQYrAKt/UjtIUOGUFdXx5QpU/qk47O+XL58meLiYj74eixgmmFTWlrKkiVL2Lx5M/fff3+vj5eRkcGwYcN47LHH2gTOsGHDWLt2bZvvzcnJITY2lszMTK5cuUJISAh5eXkmtcF4AOhy4JhuT5E7THFxMXPmzMHHx4cJEyawZcsWAKqqqggNDWXMmDGEhoZSXd39E4qpsbCwYO7cufzpT3/i9OnTJCQkcPLkSUJDQ4mNjeUf//iH3t+nlZUV7u7uTJs2DScnJ65fv46FhQVZWVlcunSJ2traDsvjTVlJSQkVFRXcd9991Giq9Ro2Bz6bppewKSkp0WvYAMyePRt7e/sufe/evXuJiYnB0tISDw8PvLy8yMzM1Ms6hO4TgWMizM3Neeedd8jNzeXo0aNs376dnJwcNm7cyNy5c8nPz2fu3Lls3Lixr5eqV2ZmZgQFBfH2229z8uRJ/vCHP1BaWsqiRYuIjIxkx44dXL16VW9hUFRURE1NDUFBQUydOpUpU6ZgZWVFYWEhR48eJS8vj5qaGpMPn+LiYsrLy5k8eXKPP63fKmz0oaSkhOjoaLZs2aK3sLmVbdu2MWnSJOLj45UPLJ31RRP6hggcE+Hq6qrM3LC2tsbHx4fS0lL27t1LXFwcAHFxcaSmpvblMg3KzMwMX19f1q9fz7Fjx/jLX/5CU1MTcXFxzJs3jy1btlBQUNCjMJBHNdy4cYNJkyYpJ2m5Hc2kSZP41a9+hZ2dHaWlpRw9epScnBwqKirQ6XT6fqu9Z/v70AAADyJJREFUUlRURGVlJX5+fsr7SH3fu1vHMHTYFBcXs2TJErZu3crs2bP1csxbeeqpp7h06RLZ2dm4urryf//3f4DY1G1qRKcBE9SVjrYDnUqlYvTo0Tz//POsXbuWq1evkpqaypo1a6iurmb+/Pmo1Wp8fHxuW24tb1Q1MzNjwoQJnZ5wWrejaT1SOz8/v8cjtfVJkiQKCwuV0OxpmbkxwiY6Oppt27Yxc+ZMvRzzdlp3hXjiiScIDw8HRF80UyOucExMVzva3klUKhWurq489dRTHDhwgAMHDjBmzBgSExOZOXMmr7zyCseOHUOr1f7i7+p0Os6cOYOlpSXe3t5d/nRrZmaGvb0948aNIygoiFGjRlFbW8vx48fJysqitLSUpqYmfb/VTkmSxMWLF6mvr+/VnqbOwmbDC2ZkZmYqgdbTW4o//vgj0dHRbN++3WhhAz93LpClpKQwceJE4Oe+aHv27KGxsZHCwkLy8/P51a9+ZbR1CW2JKjUT0tzcTHh4OPPmzVOaDLYe/tR6SJTws7q6Or7++muSk5PJzs5mxowZqNVqZs6cSUNDA9u3b2fp0qWMHDlSr6/ZfqS2k5MTQ4cO1dtrtCZJEnl5eWi1Wnx8fG4Zmg+t7Pzfxu2ubJqamqioqFA6HTg4OODk5NTlTtCXL18mNjaW7du3M2PGjNt+f0/FxsZy+PBhKioqcHFx4fXXX+fw4cNkZ2ejUqlwd3fn/fffV+4MvPHGG+zcuRNzc3M2b96slymiQhuiLLq/kSSJuLg47O3t2bx5s/L1559/HgcHB2UMblVVFW+99VYfrtR0NTU18d1335GcnExGRgZNTU0sXLiQ9evXGywM2o/UlnuhDRs2TC/HlySJ8+fPY2ZmxtixY2974u8scLp7G02r1VJZWUl5ebnS6UDu4NDR1dXly5eJiYnhz3/+s+gacOcRgdPffP/998yaNavN7ZLExEQCAwNZsmQJP/74o9LRtqsloXeqa9euoVariYyMpKKigkOHDuHl5UV4eDjz58/HxsbGIK8r90LTaDQ0NDTg4ODQq5HakiSRk5PD4MGDu9yXrqPA6e0zG51Op3RwaN3pwNbWlqFDh1JUVERsbCzvv/8+QUFBXTqmMKCIwBHuXMuWLWPFihXMmTMH+PmEeerUKZKTk0lPT8fBwUEZreDk5GSQqiX5CkGj0fRopLZOp+PcuXNYWVnh6enZrTW2Dh19Fwi07uDw3HPPUVtbS01NDZs2bUKtVvfomEK/JwJHuHNJktTpCVouj05OTmbfvn2Ym5sTFhZGZGQkbm5uBgmf1iO1a2pqbjtSWy50sLGx6fK00dbkwDF0NVpRURHLly9n5syZnDp1ioaGBn7zm9+wYsUKvRxf6DdE4AjC7UiSRGlpKSkpKaSmpnLjxg0WLFhAREQE48aNM0j4tB6pXVlZ+YuR2lqtltOnT+Pg4NDjQocHo//b6Z/pK2wKCwtZunQpO3bsUKq+KisrKSwsJCAgQC+vIfQbInAEobsqKir44osvSElJoaSkhJCQENRqdZfHZXdX6+mfcsVbY2Mj99xzDx4eHr06dkeho6+wKSgoYNmyZXzwwQdMm9b7Y3bUjLOqqoro6GiKiopwd3fn888/VyamJiQkkJaWhpWVFbt27VI2TAt9RvRSE/RDq9Xi7++vbKQrLCwkMDCQMWPGEB0dbdS9KIbm6OhIfHw8+/btIyMjg4CAALZt28Z9993H2rVrycjIoKWlRW+vJ4/U9vT0ZMqUKWi1WoYPH05lZSX//e9/KSoqoq6uTi+vpa+wuXTpkl7DBmD58uWkp6e3+VpnLZ2++uor8vPzyc/P569//StPPfWUXtYgGIe4whFuadOmTRw/fpzr16/z5ZdfsmTJEh5++GFiYmL47W9/i5+f34D/pW9sbOSbb74hJSWFo0ePEhAQgFqtJjg4WC9jDZqbm8nOzubee+/l7rvvBvQzUlu+ytFX2Fy8eJFHH32UnTt36v22WVFREeHh4coVTmf7z1auXElwcDCxsbG/+D6hz4grHKH3SkpK2L9/v/IQWJIkvv32W6KiooCB39tNZmlpSVhYGB988AHZ2dksX76cw4cPc//99xMXF0dycjK1tbU9OnZTUxNZWVmMGjVKCRuAwYMHM2LECPz9/QkICMDa2prLly9z9OhRLly4QFVVVZe6AegrbPLz83n00Uf56KOPjPKMprOWTqIZZ/8meqkJnVq9ejVvvfWWcjKtrKzE1tZW6SV2J/6ym5ubExwcTHBwMDqdjpMnT5KUlMSmTZtwdXVVyq0dHBxue6zGxkays7MZPXo0jo6Ot3xNFxcXXFxclJHaV69e5cKFC7ccqa3PsHnsscdM4nmJaMbZv4nAETokP8SdOnUqhw8fBsQve3tmZmYEBAQQEBBAYmIiubm5JCcns2TJEoYOHUpYWBhqtZp77rnnF/+fGhoayM7OZuzYsd3ayGtmZoajoyOOjo5tRk9fvHhR2ZDp5OSktwajeXl5xMXF8dFHHxk1bFxcXCgrK1NuqTk7OwOiGWd/J26pCR06cuQIX3zxBe7u7sTExPDtt9+yevVqampqlAfn4pf9f1QqFePHj+eVV17hhx9+YOfOnZiZmfHEE08QEhLCO++8Q35+vtIXbffu3YwbN65XXSNUKhV2dnZ4e3sTFBSEh4cH9fX1nDhxgpMnT1JSUkJjY2OPjy+HTV9c2ajVanbv3g3A7t27iYyMVL7+t7/9DUmSOHr0KDY2NuL5TT8iigaE2zp8+DB//OMf+fLLL1m8eDGPPPKIUjQwadIknn766b5eosmSJIny8nJSU1NJTU3l8uXL1NbWsm7dOpYtW2aQcmv45UhtZ2dnnJ2du9xT7sKFC8TFxfG3v/2NyZMnG2SNso6acT700EMdtnSSJIlVq1aRnp6OlZWV0Z4pCbck9uEI+tM6cAoKCoiJiaGqqgp/f38+/vhjLC0t+3qJ/UJubi5Llixh6dKlnDx5kgsXLhAcHIxarSYwMLDHkztvp7GxUal4a25ubtNgtKNboufPn2f58uVGCRthQBCBIwimpKmpiTlz5rBjxw7Gjx8PwM2bNzl48CBJSUmcOHGCoKAg1Go1s2fPZvDgwQZZR3NzszKCoK6urk2DUTMzMyVs/v73v+Pn52eQNQgDjggcQTA1zc3NWFhYdPpnGRkZJCUl8e9//5uJEyeiVqsJCQnhrrvuMsh6tFotVVVVlJWVER8fj6enJ+fPn+ezzz5j6tSpBnlNYUASgSMI/ZVOpyMzM5OkpCQOHjzIqFGjCA8PZ+HChdjZ2RnkNU+dOsWaNWsYPXo0Z86cYeLEiW06bgvCLYjAEYSBQB5TkJyczP79+7GxsSE8PJyIiAhcXFz0Upaek5NDfHw8//jHP/D19UWSJLKysqirq2PWrFl6eBfCACcCRxiYampqWLFiBWfPnkWlUrFz5068vb07bPQ40EiSREFBASkpKezduxdJkggLCyMiIgIPD48ehY8cNp988gkTJ07U+5rd3d2xtrZm0KBBmJubc/z48U4bcwr9lggcYWCKi4tj1qxZrFixgqamJurr60lMTMTe3l4Zw11dXc2bb77Z10s1KEmSuHr1KqmpqaSkpFBdXc28efOIjIzEx8enS+XW586d4/HHHzdY2MDPgXP8+PE2nRReeOGFO+7nNcCJwBEGnuvXr+Pn50dBQUGbT/OdNXq8k1RXV7Nv3z5SUlIoLCzkgQceICIigoCAgA7LreWw+fTTT5kwYYLB1tVR4Iif14AjAkcYeLKzs3nyyScZP348p06dYurUqWzZsoURI0ZQU1OjfJ+dnR3V1dV9uNK+VV9fT3p6OsnJyWRnZzNjxgzUajUzZ87EwsKCs2fPsmLFCvbs2aOUaBuKh4cHdnZ2qFQqVq5cyZNPPomtra34eQ0sInCEgef48eMEBQVx5MgRAgMDSUhIYPjw4bz33nviBNaJpqYmvvvuO5KTkzly5Aju7u7k5eWRmppq8LABuHLlCvfccw8ajYbQ0FDee+891Gq1+HkNLF0OHNG8U+g33NzccHNzIzAwEICoqCg2btzYaaNH4ecxB/PmzWPevHlotVr++c9/YmNjY5SwAZRee87OzixatIjMzEzx87qDieadQr9x9913c++99yr3+w8dOsT48eM7bfQotDVo0CBiYmJYsGCBUV6vrq5OGW1RV1fHgQMHlA2t4ud1ZxK31IR+JTs7W6lQ8/T05KOPPkKn03XY6FHoWwUFBSxatAiAlpYWli5dyrp166isrBQ/r4FFPMMRBEEQjEKMmBYEQRBMiwgcQRAEwShE4AiCIAhGIQJHEPTg3XffZcKECUycOJHY2FgaGhooLCwkMDCQMWPGEB0dTVNTU18vUxD6lAgcQeil0tJStm7dyvHjxzl79ixarZY9e/bw4osv8rvf/Y78/Hzs7Oz48MMP+3qpepOeno63tzdeXl5s3Lixr5cj9BMicARBD1paWrh58yYtLS3U19fj6urKt99+S1RUFPBz09HU1NQ+XqV+aLVannnmGb766itycnL49NNPycnJ6etlCf2ACBxB6KURI0awdu1aRo4ciaurKzY2NkydOhVbW1vMzX9u5uHm5kZpaWkfr1Q/MjMz8fLywtPTk8GDBxMTE8PevXv7ellCPyACRxB6qbq6mr1791JYWMiVK1eoq6vjq6+++sX36WNYmikoLS3l3nvvVf57IIWpYFiil5og9NI333yDh4cHTk5OADz88MP88MMP1NTU0NLSgrm5OSUlJUpfsf6uo83iAyVMBcMSVziC0EsjR47k6NGj1NfXI0mS0uNtzpw5/Otf/wIGVs8wNzc3iouLlf8eSGEqGJZobSMIevDaa6/x2WefYW5ujr+/Px988AGlpaXExMRQVVWFv78/H3/8MZaWln291F5raWlh7NixHDp0iBEjRjBt2jQ++eQTgw5yE0ya6KUmCILhpKWlsXr1arRaLfHx8axbt66vlyT0HRE4giAIglGI5p2CIAiCaRGBIwiCIBiFCBxBEATBKETgCIIgCEYhAkcQBEEwChE4giAIglF0t7WN6F8hCIIg9Ii4whEEQRCMQgSOIAiCYBQicARBEASjEIEjCIIgGIUIHEEQBMEoROAIgiAIRiECRxAEQTAKETiCIAiCUYjAEQRBEIxCBI4gCIJgFP8PqT/X9g/9tZYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_scalar_field(landing_distance,0,90,0,360)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.3 Finding the uphill direction with the gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def secant_slope(f,xmin,xmax): #<1>\n",
    "    return (f(xmax) - f(xmin)) / (xmax - xmin)\n",
    "\n",
    "def approx_derivative(f,x,dx=1e-6): #<2>\n",
    "    return secant_slope(f,x-dx,x+dx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def approx_gradient(f,x0,y0,dx=1e-6):\n",
    "    partial_x = approx_derivative(lambda x: f(x,y0), x0, dx=dx)\n",
    "    partial_y = approx_derivative(lambda y: f(x0,y), y0, dx=dx)\n",
    "    return (partial_x,partial_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def landing_distance_gradient(theta,phi):\n",
    "    return approx_gradient(landing_distance, theta, phi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Feel free to ignore the following code, which just supports the graphic of overlaying a vector field on a heatmap."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 504x504 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from vectors import to_polar, to_cartesian\n",
    "\n",
    "def draw_arrow(tip,tail,color='k'):\n",
    "    tip_length = (plt.xlim()[1] - plt.xlim()[0]) / 20.\n",
    "    length = sqrt((tip[1]-tail[1])**2 + (tip[0]-tail[0])**2)\n",
    "    new_length = length - tip_length\n",
    "    new_y = (tip[1] - tail[1]) * (new_length / length)\n",
    "    new_x = (tip[0] - tail[0]) * (new_length / length)\n",
    "    plt.gca().arrow(tail[0], tail[1], new_x, new_y,\n",
    "    head_width=tip_length/1.5, \n",
    "    head_length=tip_length/2,\n",
    "    fc=color, ec=color)\n",
    "    \n",
    "def plot_vector_field(f,xmin,xmax,ymin,ymax,xsteps=10,ysteps=10,color='k'):\n",
    "\n",
    "    X,Y = np.meshgrid(np.linspace(xmin,xmax, xsteps),np.linspace(ymin,ymax, ysteps))\n",
    "    U = np.vectorize(lambda x,y : f(x,y)[0])(X,Y)\n",
    "    V = np.vectorize(lambda x,y : f(x,y)[1])(X,Y)\n",
    "    plt.quiver(X, Y, U, V,color=color)\n",
    "    fig = plt.gcf()\n",
    "\n",
    "scalar_field_heatmap(landing_distance,0,90,0,360)\n",
    "plot_vector_field(landing_distance_gradient,0,90,0,360,xsteps=10,ysteps=10,color='k')\n",
    "plt.xlabel('theta')\n",
    "plt.ylabel('phi')\n",
    "plt.gcf().set_size_inches(9,7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 504x504 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scalar_field_heatmap(landing_distance,35,40,80,100)\n",
    "plot_vector_field(landing_distance_gradient,35,40,80,100,xsteps=10,ysteps=15,color='k')\n",
    "plt.xlabel('theta')\n",
    "plt.ylabel('phi')\n",
    "plt.gcf().set_size_inches(9,7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.4 Implementing gradient ascent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "from vectors import length\n",
    "\n",
    "def gradient_ascent(f,xstart,ystart,tolerance=1e-6):\n",
    "    x = xstart\n",
    "    y = ystart\n",
    "    grad = approx_gradient(f,x,y)\n",
    "    while length(grad) > tolerance:\n",
    "        x += grad[0]\n",
    "        y += grad[1]\n",
    "        grad = approx_gradient(f,x,y)\n",
    "    return x,y\n",
    "\n",
    "def gradient_ascent_points(f,xstart,ystart,tolerance=1e-6):\n",
    "    x = xstart\n",
    "    y = ystart\n",
    "    xs, ys = [x], [y]\n",
    "    grad = approx_gradient(f,x,y)\n",
    "    while length(grad) > tolerance:\n",
    "        x += grad[0]\n",
    "        y += grad[1]\n",
    "        grad = approx_gradient(f,x,y)\n",
    "        xs.append(x)\n",
    "        ys.append(y)\n",
    "    return xs, ys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(37.58114751557887, 89.99992616039857)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient_ascent(landing_distance,36,83)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_ascent_points(f,xstart,ystart,tolerance=1e-6):\n",
    "    x = xstart\n",
    "    y = ystart\n",
    "    xs, ys = [x], [y]\n",
    "    grad = approx_gradient(f,x,y)\n",
    "    while length(grad) > tolerance:\n",
    "        x += grad[0]\n",
    "        y += grad[1]\n",
    "        grad = approx_gradient(f,x,y)\n",
    "        xs.append(x)\n",
    "        ys.append(y)\n",
    "    return xs, ys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  89.99992515853332,\n",
       "  89.99992616039857])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient_ascent_points(landing_distance,36,83)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 504x504 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from vectors import to_polar, to_cartesian\n",
    "scalar_field_heatmap(landing_distance,35,40,80,100)\n",
    "plt.scatter([36,37.58114751557887],[83,89.99992616039857],c='k',s=75)\n",
    "plt.plot(*gradient_ascent_points(landing_distance,36,83),c='k')\n",
    "plt.xlabel('theta')\n",
    "plt.ylabel('phi')\n",
    "plt.gcf().set_size_inches(9,7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "52.98310689354378"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "landing_distance(37.58114751557887, 89.99992616039857)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.5 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** On the heatmap, simultaneously plot the paths of gradient ascent from 20 randomly chosen points.  All of the paths should end up at one of the two maxima."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 504x504 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scalar_field_heatmap(landing_distance,0,90,0,360)\n",
    "plt.xlabel('theta')\n",
    "plt.ylabel('phi')\n",
    "gap = gradient_ascent_points(landing_distance,60,190,1000)\n",
    "\n",
    "from random import uniform\n",
    "for x in range(0,20):\n",
    "    gap = gradient_ascent_points(landing_distance,uniform(0,90),uniform(0,360))\n",
    "    plt.plot(*gap,c='k')\n",
    "plt.gcf().set_size_inches(9,7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Find the point on $r(\\theta,\\phi)$ where the gradient is zero but the function is not maximized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(46.122613357930206, 180.0)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient_ascent(landing_distance,0,180)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** How many steps does it take for gradient ascent to reach the origin from (36,83)?  Instead of jumping one gradient, jump 1.5 gradients.  Show that you get there in fewer steps.  What happens if you jump even further in each step?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_ascent_points(f,xstart,ystart,rate=1,tolerance=1e-6):\n",
    "    x = xstart\n",
    "    y = ystart\n",
    "    xs, ys = [x], [y]\n",
    "    grad = approx_gradient(f,x,y)\n",
    "    while length(grad) > tolerance:\n",
    "        x += rate * grad[0]\n",
    "        y += rate * grad[1]\n",
    "        grad = approx_gradient(f,x,y)\n",
    "        xs.append(x)\n",
    "        ys.append(y)\n",
    "    return xs, ys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "def count_ascent_steps(f,x,y,rate=1):\n",
    "    gap = gradient_ascent_points(f,x,y,rate=rate)\n",
    "    print(gap[0][-1],gap[1][-1])\n",
    "    return len(gap[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "37.58114751557887 89.99992616039857\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "855"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_ascent_steps(landing_distance,36,83)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "37.58114755288237 89.99992556887184\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "568"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_ascent_steps(landing_distance,36,83,rate=1.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "37.58114749426255 89.99992676791281\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "282"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_ascent_steps(landing_distance,36,83,rate=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "37.58114748360439 89.99992495958149\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "81"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_ascent_steps(landing_distance,36,83,rate=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "37.58114744807723 89.99992670041118\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "38"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_ascent_steps(landing_distance,36,83,rate=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 504x504 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scalar_field_heatmap(landing_distance,35,40,80,100)\n",
    "plt.scatter([36,37.58114751557887],[83,89.99992616039857],c='k',s=75)\n",
    "plt.plot(*gradient_ascent_points(landing_distance,36,83,rate=20),c='k')\n",
    "plt.xlabel('theta')\n",
    "plt.ylabel('phi')\n",
    "plt.gcf().set_size_inches(9,7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** What happens when you try to run gradient_ascent directly using simulated results for $r$  as a function of $\\theta$ and $\\phi$ instead of calculated results?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulated_distance_270(theta):\n",
    "    ts,xs,ys,zs = trajectory3d(theta,270)\n",
    "    return sqrt(xs[-1]**2 + ys[-1]**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_function(simulated_distance_270,35,45)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
